prediccion precios OPEP.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31mRunning cells with 'Python 3.11.9' requires the ipykernel package.\n",
      "\u001b[1;31mRun the following command to install 'ipykernel' into the Python environment. \n",
      "\u001b[1;31mCommand: '\"c:/Users/Patricia García/AppData/Local/Microsoft/WindowsApps/PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0/python.exe\" -m pip install ipykernel -U --user --force-reinstall'"
     ]
    }
   ],
   "source": [
    "#Practica de git + git hub\n",
    "print(\"primer cambio en el cuaderno .ipynb\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.tsa.statespace.sarimax import SARIMAX\n",
    "import warnings\n",
    "from sklearn.model_selection import TimeSeriesSplit\n",
    "from sklearn.model_selection import ParameterSampler\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.gridspec as gridspec\n",
    "import plotly.express as px\n",
    "\n",
    "warnings.filterwarnings('ignore')  # Ignore warning messages\n",
    "\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Union de los datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Fecha Precio $\n",
      "0    02/01/2019  52,14Ê$\n",
      "1    03/01/2019  52,93Ê$\n",
      "2    04/01/2019  55,13Ê$\n",
      "3    07/01/2019  56,42Ê$\n",
      "4    08/01/2019  56,09Ê$\n",
      "..          ...      ...\n",
      "253  24/12/2019  67,99Ê$\n",
      "254  26/12/2019  68,48Ê$\n",
      "255  27/12/2019  69,07Ê$\n",
      "256  30/12/2019  68,89Ê$\n",
      "257  31/12/2019  67,96Ê$\n",
      "\n",
      "[258 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Ruta del archivo CSV (ajusta la ruta según sea necesario)\n",
    "OPEP2019 = \"DATA/data_2019.csv\"\n",
    "\n",
    "# Leer el archivo CSV utilizando pandas\n",
    "df1 = pd.read_csv(OPEP2019, sep=';', decimal='�', encoding='latin-1')\n",
    "\n",
    "# Mostrar el DataFrame para verificar que los datos se han cargado correctamente\n",
    "print(df1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Fecha Precio $\n",
      "0    2019-01-02  52,14 $\n",
      "1    2019-01-03  52,93 $\n",
      "2    2019-01-04  55,13 $\n",
      "3    2019-01-07  56,42 $\n",
      "4    2019-01-08  56,09 $\n",
      "..          ...      ...\n",
      "253  2019-12-24  67,99 $\n",
      "254  2019-12-26  68,48 $\n",
      "255  2019-12-27  69,07 $\n",
      "256  2019-12-30  68,89 $\n",
      "257  2019-12-31  67,96 $\n",
      "\n",
      "[258 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "df1['Precio $'] = df1['Precio $'].str.replace('Ê', ' ')\n",
    "\n",
    "df1['Fecha'] = pd.to_datetime(df1['Fecha'], format='%d/%m/%Y').dt.strftime('%Y-%m-%d')\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Fecha Precio $\n",
      "0    2019-01-02   52,14 \n",
      "1    2019-01-03   52,93 \n",
      "2    2019-01-04   55,13 \n",
      "3    2019-01-07   56,42 \n",
      "4    2019-01-08   56,09 \n",
      "..          ...      ...\n",
      "253  2019-12-24   67,99 \n",
      "254  2019-12-26   68,48 \n",
      "255  2019-12-27   69,07 \n",
      "256  2019-12-30   68,89 \n",
      "257  2019-12-31   67,96 \n",
      "\n",
      "[258 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "df1['Precio $'] = df1['Precio $'].str.replace('\\$', '', regex=True)\n",
    "\n",
    "print(df1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          FECHA  PRECIO\n",
      "0    2019-01-02  52,14 \n",
      "1    2019-01-03  52,93 \n",
      "2    2019-01-04  55,13 \n",
      "3    2019-01-07  56,42 \n",
      "4    2019-01-08  56,09 \n",
      "..          ...     ...\n",
      "253  2019-12-24  67,99 \n",
      "254  2019-12-26  68,48 \n",
      "255  2019-12-27  69,07 \n",
      "256  2019-12-30  68,89 \n",
      "257  2019-12-31  67,96 \n",
      "\n",
      "[258 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Renombrar las columnas 'Fecha' y 'Precio $'\n",
    "df1 = df1.rename(columns={'Fecha': 'FECHA', 'Precio $': 'PRECIO'})\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         Fecha  Precio USD/BBL\n",
      "0    2020-01-02        67,12 $\n",
      "1    2020-01-03        69,38 $\n",
      "2    2020-01-06        70,87 $\n",
      "3    2020-01-07        69,60 $\n",
      "4    2020-01-08        69,58 $\n",
      "..          ...            ...\n",
      "234  2020-11-24        45,51 $\n",
      "235  2020-11-25        46,91 $\n",
      "236  2020-11-26        46,66 $\n",
      "237  2020-11-27        46,79 $\n",
      "238  2020-11-30        46,43 $\n",
      "\n",
      "[239 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Ruta del archivo CSV (ajusta la ruta según sea necesario)\n",
    "OPEP2020 = \"/Users/leidygarciaguzman/Documents/PRECIO OPEP /DATA/OPEP 2020.csv\"\n",
    "\n",
    "# Leer el archivo CSV utilizando pandas\n",
    "df2 = pd.read_csv(OPEP2020, sep=';', decimal=',')\n",
    "\n",
    "# Mostrar el DataFrame para verificar que los datos se han cargado correctamente\n",
    "print(df2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         Fecha  Precio USD/BBL\n",
      "0    2020-01-02         67,12 \n",
      "1    2020-01-03         69,38 \n",
      "2    2020-01-06         70,87 \n",
      "3    2020-01-07         69,60 \n",
      "4    2020-01-08         69,58 \n",
      "..          ...            ...\n",
      "234  2020-11-24         45,51 \n",
      "235  2020-11-25         46,91 \n",
      "236  2020-11-26         46,66 \n",
      "237  2020-11-27         46,79 \n",
      "238  2020-11-30         46,43 \n",
      "\n",
      "[239 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Eliminar el signo '$' de toda la columna 'Precio USD/BBL'\n",
    "df2['Precio USD/BBL'] = df2['Precio USD/BBL'].str.replace('\\$', '', regex=True)\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Fecha ', 'Precio USD/BBL'], dtype='object')"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.columns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          FECHA  PRECIO\n",
      "0    2020-01-02  67,12 \n",
      "1    2020-01-03  69,38 \n",
      "2    2020-01-06  70,87 \n",
      "3    2020-01-07  69,60 \n",
      "4    2020-01-08  69,58 \n",
      "..          ...     ...\n",
      "234  2020-11-24  45,51 \n",
      "235  2020-11-25  46,91 \n",
      "236  2020-11-26  46,66 \n",
      "237  2020-11-27  46,79 \n",
      "238  2020-11-30  46,43 \n",
      "\n",
      "[239 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Renombrar las columnas 'Fecha' y 'Precio $'\n",
    "df2 = df2.rename(columns={'Fecha ': 'FECHA', 'Precio USD/BBL': 'PRECIO'})\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Fecha Precio $\n",
      "0    04/01/2021  51,35Ê$\n",
      "1    05/01/2021  50,75Ê$\n",
      "2    06/01/2021  53,29Ê$\n",
      "3    07/01/2021  53,84Ê$\n",
      "4    08/01/2021  54,39Ê$\n",
      "..          ...      ...\n",
      "254  27/12/2021  75,63Ê$\n",
      "255  28/12/2021  77,39Ê$\n",
      "256  29/12/2021  78,17Ê$\n",
      "257  30/12/2021  78,33Ê$\n",
      "258  31/12/2021  77,97Ê$\n",
      "\n",
      "[259 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Ruta del archivo CSV (ajusta la ruta según sea necesario)\n",
    "OPEP2021 = \"DATA/data_2021.csv\"\n",
    "\n",
    "# Leer el archivo CSV utilizando pandas\n",
    "df3 = pd.read_csv(OPEP2021, sep=';', decimal='�', encoding='latin-1')\n",
    "\n",
    "# Mostrar el DataFrame para verificar que los datos se han cargado correctamente\n",
    "print(df3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Fecha Precio $\n",
      "0    04/01/2021  51,35 $\n",
      "1    05/01/2021  50,75 $\n",
      "2    06/01/2021  53,29 $\n",
      "3    07/01/2021  53,84 $\n",
      "4    08/01/2021  54,39 $\n",
      "..          ...      ...\n",
      "254  27/12/2021  75,63 $\n",
      "255  28/12/2021  77,39 $\n",
      "256  29/12/2021  78,17 $\n",
      "257  30/12/2021  78,33 $\n",
      "258  31/12/2021  77,97 $\n",
      "\n",
      "[259 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "df3['Precio $'] = df3['Precio $'].str.replace('Ê', ' ')\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Fecha Precio $\n",
      "0    2021-01-04   51,35 \n",
      "1    2021-01-05   50,75 \n",
      "2    2021-01-06   53,29 \n",
      "3    2021-01-07   53,84 \n",
      "4    2021-01-08   54,39 \n",
      "..          ...      ...\n",
      "254  2021-12-27   75,63 \n",
      "255  2021-12-28   77,39 \n",
      "256  2021-12-29   78,17 \n",
      "257  2021-12-30   78,33 \n",
      "258  2021-12-31   77,97 \n",
      "\n",
      "[259 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Eliminar el signo '$' de toda la columna 'Precio $'\n",
    "df3['Precio $'] = df3['Precio $'].str.replace('\\$', '', regex=True)\n",
    "\n",
    "df3['Fecha'] = pd.to_datetime(df3['Fecha'], format='%d/%m/%Y').dt.strftime('%Y-%m-%d')\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          FECHA  PRECIO\n",
      "0    2021-01-04  51,35 \n",
      "1    2021-01-05  50,75 \n",
      "2    2021-01-06  53,29 \n",
      "3    2021-01-07  53,84 \n",
      "4    2021-01-08  54,39 \n",
      "..          ...     ...\n",
      "254  2021-12-27  75,63 \n",
      "255  2021-12-28  77,39 \n",
      "256  2021-12-29  78,17 \n",
      "257  2021-12-30  78,33 \n",
      "258  2021-12-31  77,97 \n",
      "\n",
      "[259 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Renombrar las columnas 'Fecha' y 'Precio $'\n",
    "df3 = df3.rename(columns={'Fecha': 'FECHA', 'Precio $': 'PRECIO'})\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Unnamed: 0 Unnamed: 1  Unnamed: 2\n",
      "0    2022-01-03    78,00 $         NaN\n",
      "1    2022-01-04    78,93 $         NaN\n",
      "2    2022-01-05    80,07 $         NaN\n",
      "3    2022-01-06    80,80 $         NaN\n",
      "4    2022-01-07    82,16 $         NaN\n",
      "..          ...        ...         ...\n",
      "253  2022-12-23    80,58 $         NaN\n",
      "254  2022-12-27    82,23 $         NaN\n",
      "255  2022-12-28    81,96 $         NaN\n",
      "256  2022-12-29    80,39 $         NaN\n",
      "257  2022-12-30    81,29 $         NaN\n",
      "\n",
      "[258 rows x 3 columns]\n"
     ]
    }
   ],
   "source": [
    "# Ruta del archivo CSV (ajusta la ruta según sea necesario)\n",
    "OPEP2022 = \"/Users/leidygarciaguzman/Documents/PRECIO OPEP /DATA/OPEP 2022.csv\"\n",
    "\n",
    "# Leer el archivo CSV utilizando pandas\n",
    "df4 = pd.read_csv(OPEP2022, sep=';', decimal=',')\n",
    "\n",
    "# Mostrar el DataFrame para verificar que los datos se han cargado correctamente\n",
    "print(df4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          FECHA   PRECIO\n",
      "0    2022-01-03  78,00 $\n",
      "1    2022-01-04  78,93 $\n",
      "2    2022-01-05  80,07 $\n",
      "3    2022-01-06  80,80 $\n",
      "4    2022-01-07  82,16 $\n",
      "..          ...      ...\n",
      "253  2022-12-23  80,58 $\n",
      "254  2022-12-27  82,23 $\n",
      "255  2022-12-28  81,96 $\n",
      "256  2022-12-29  80,39 $\n",
      "257  2022-12-30  81,29 $\n",
      "\n",
      "[258 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Eliminar la columna \"Unnamed: 2\"\n",
    "df4.drop(columns=['Unnamed: 2'], inplace=True)\n",
    "\n",
    "# Renombrar las columnas\n",
    "df4.rename(columns={'Unnamed: 0': 'FECHA', 'Unnamed: 1': 'PRECIO'}, inplace=True)\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          FECHA  PRECIO\n",
      "0    2022-01-03  78,00 \n",
      "1    2022-01-04  78,93 \n",
      "2    2022-01-05  80,07 \n",
      "3    2022-01-06  80,80 \n",
      "4    2022-01-07  82,16 \n",
      "..          ...     ...\n",
      "253  2022-12-23  80,58 \n",
      "254  2022-12-27  82,23 \n",
      "255  2022-12-28  81,96 \n",
      "256  2022-12-29  80,39 \n",
      "257  2022-12-30  81,29 \n",
      "\n",
      "[258 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Eliminar el signo '$' de toda la columna 'Precio $'\n",
    "df4['PRECIO'] = df4['PRECIO'].str.replace('\\$', '', regex=True)\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Fecha Precio $\n",
      "0    03/01/2023  82,07Ê$\n",
      "1    04/01/2023  76,90Ê$\n",
      "2    05/01/2023  75,79Ê$\n",
      "3    06/01/2023  76,15Ê$\n",
      "4    09/01/2023  77,57Ê$\n",
      "..          ...      ...\n",
      "142  21/07/2023  81,99Ê$\n",
      "143  24/07/2023  83,19Ê$\n",
      "144  25/07/2023  84,64Ê$\n",
      "145  26/07/2023  84,82Ê$\n",
      "146  27/07/2023  84,88Ê$\n",
      "\n",
      "[147 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Ruta del archivo CSV (ajusta la ruta según sea necesario)\n",
    "OPEP2023 = \"/Users/leidygarciaguzman/Documents/PRECIO OPEP /DATA/data_2023.csv\"\n",
    "\n",
    "# Leer el archivo CSV utilizando pandas\n",
    "df5 = pd.read_csv(OPEP2023, sep=';', decimal='�', encoding='latin-1')\n",
    "\n",
    "# Mostrar el DataFrame para verificar que los datos se han cargado correctamente\n",
    "print(df5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Fecha Precio $\n",
      "0    03/01/2023  82,07 $\n",
      "1    04/01/2023  76,90 $\n",
      "2    05/01/2023  75,79 $\n",
      "3    06/01/2023  76,15 $\n",
      "4    09/01/2023  77,57 $\n",
      "..          ...      ...\n",
      "142  21/07/2023  81,99 $\n",
      "143  24/07/2023  83,19 $\n",
      "144  25/07/2023  84,64 $\n",
      "145  26/07/2023  84,82 $\n",
      "146  27/07/2023  84,88 $\n",
      "\n",
      "[147 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "df5['Precio $'] = df5['Precio $'].str.replace('Ê', ' ')\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Fecha Precio $\n",
      "0    2023-01-03   82,07 \n",
      "1    2023-01-04   76,90 \n",
      "2    2023-01-05   75,79 \n",
      "3    2023-01-06   76,15 \n",
      "4    2023-01-09   77,57 \n",
      "..          ...      ...\n",
      "142  2023-07-21   81,99 \n",
      "143  2023-07-24   83,19 \n",
      "144  2023-07-25   84,64 \n",
      "145  2023-07-26   84,82 \n",
      "146  2023-07-27   84,88 \n",
      "\n",
      "[147 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Eliminar el signo '$' de toda la columna 'Precio $'\n",
    "df5['Precio $'] = df5['Precio $'].str.replace('\\$', '', regex=True)\n",
    "\n",
    "df5['Fecha'] = pd.to_datetime(df5['Fecha'], format='%d/%m/%Y').dt.strftime('%Y-%m-%d')\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          FECHA  PRECIO\n",
      "0    2023-01-03  82,07 \n",
      "1    2023-01-04  76,90 \n",
      "2    2023-01-05  75,79 \n",
      "3    2023-01-06  76,15 \n",
      "4    2023-01-09  77,57 \n",
      "..          ...     ...\n",
      "142  2023-07-21  81,99 \n",
      "143  2023-07-24  83,19 \n",
      "144  2023-07-25  84,64 \n",
      "145  2023-07-26  84,82 \n",
      "146  2023-07-27  84,88 \n",
      "\n",
      "[147 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Renombrar las columnas 'Fecha' y 'Precio $'\n",
    "df5 = df5.rename(columns={'Fecha': 'FECHA', 'Precio $': 'PRECIO'})\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(df5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    UNIMOS LOS 5 DATAFRAME "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          FECHA  PRECIO\n",
      "0    2019-01-02  52,14 \n",
      "1    2019-01-03  52,93 \n",
      "2    2019-01-04  55,13 \n",
      "3    2019-01-07  56,42 \n",
      "4    2019-01-08  56,09 \n",
      "..          ...     ...\n",
      "142  2023-07-21  81,99 \n",
      "143  2023-07-24  83,19 \n",
      "144  2023-07-25  84,64 \n",
      "145  2023-07-26  84,82 \n",
      "146  2023-07-27  84,88 \n",
      "\n",
      "[1161 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Crea una lista con los DataFrames que deseas unir\n",
    "df = [df1, df2, df3, df4, df5]\n",
    "\n",
    "# Concatena los DataFrames en orden por años\n",
    "OPEP = pd.concat(df)\n",
    "\n",
    "# Mostrar el DataFrame resultante\n",
    "print(OPEP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploratory Data Analysis EDA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FECHA</th>\n",
       "      <th>PRECIO</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2019-01-02</td>\n",
       "      <td>52,14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2019-01-03</td>\n",
       "      <td>52,93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2019-01-04</td>\n",
       "      <td>55,13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2019-01-07</td>\n",
       "      <td>56,42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2019-01-08</td>\n",
       "      <td>56,09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2019-01-09</td>\n",
       "      <td>58,22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2019-01-10</td>\n",
       "      <td>59,46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2019-01-11</td>\n",
       "      <td>60,00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2019-01-14</td>\n",
       "      <td>58,39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2019-01-15</td>\n",
       "      <td>58,24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2019-01-16</td>\n",
       "      <td>59,52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2019-01-17</td>\n",
       "      <td>59,63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2019-01-18</td>\n",
       "      <td>60,90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2019-01-21</td>\n",
       "      <td>61,49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2019-01-22</td>\n",
       "      <td>60,66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2019-01-23</td>\n",
       "      <td>60,52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2019-01-24</td>\n",
       "      <td>60,22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2019-01-25</td>\n",
       "      <td>60,90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2019-01-28</td>\n",
       "      <td>59,57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2019-01-29</td>\n",
       "      <td>59,71</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         FECHA  PRECIO\n",
       "0   2019-01-02  52,14 \n",
       "1   2019-01-03  52,93 \n",
       "2   2019-01-04  55,13 \n",
       "3   2019-01-07  56,42 \n",
       "4   2019-01-08  56,09 \n",
       "5   2019-01-09  58,22 \n",
       "6   2019-01-10  59,46 \n",
       "7   2019-01-11  60,00 \n",
       "8   2019-01-14  58,39 \n",
       "9   2019-01-15  58,24 \n",
       "10  2019-01-16  59,52 \n",
       "11  2019-01-17  59,63 \n",
       "12  2019-01-18  60,90 \n",
       "13  2019-01-21  61,49 \n",
       "14  2019-01-22  60,66 \n",
       "15  2019-01-23  60,52 \n",
       "16  2019-01-24  60,22 \n",
       "17  2019-01-25  60,90 \n",
       "18  2019-01-28  59,57 \n",
       "19  2019-01-29  59,71 "
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP.head(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FECHA</th>\n",
       "      <th>PRECIO</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>142</th>\n",
       "      <td>2023-07-21</td>\n",
       "      <td>81,99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>143</th>\n",
       "      <td>2023-07-24</td>\n",
       "      <td>83,19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>144</th>\n",
       "      <td>2023-07-25</td>\n",
       "      <td>84,64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>2023-07-26</td>\n",
       "      <td>84,82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>2023-07-27</td>\n",
       "      <td>84,88</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          FECHA  PRECIO\n",
       "142  2023-07-21  81,99 \n",
       "143  2023-07-24  83,19 \n",
       "144  2023-07-25  84,64 \n",
       "145  2023-07-26  84,82 \n",
       "146  2023-07-27  84,88 "
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FECHA</th>\n",
       "      <th>PRECIO</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1161</td>\n",
       "      <td>1161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>1158</td>\n",
       "      <td>1077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>2020-08-31</td>\n",
       "      <td>65,60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             FECHA  PRECIO\n",
       "count         1161    1161\n",
       "unique        1158    1077\n",
       "top     2020-08-31  65,60 \n",
       "freq             2       3"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP.describe(include='all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "OPEP.to_csv('OPEP_data.csv', index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "OPEP_copia = OPEP.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1161, 2)"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['FECHA', 'PRECIO'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "# Mostrar los nombres de las columnas actuales\n",
    "print(OPEP.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1161, 2)"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP.shape "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FECHA     0.0\n",
       "PRECIO    0.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP.isna().mean()*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FECHA     0\n",
      "PRECIO    0\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# Verificar los valores faltantes en el DataFrame OPEP\n",
    "missing_values = OPEP.isnull().sum()\n",
    "\n",
    "# Mostrar el total de valores faltantes por columna\n",
    "print(missing_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 1161 entries, 0 to 146\n",
      "Data columns (total 2 columns):\n",
      " #   Column  Non-Null Count  Dtype \n",
      "---  ------  --------------  ----- \n",
      " 0   FECHA   1161 non-null   object\n",
      " 1   PRECIO  1161 non-null   object\n",
      "dtypes: object(2)\n",
      "memory usage: 27.2+ KB\n"
     ]
    }
   ],
   "source": [
    "OPEP.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            PRECIO\n",
      "FECHA             \n",
      "2019-01-02  52,14 \n",
      "2019-01-03  52,93 \n",
      "2019-01-04  55,13 \n",
      "2019-01-07  56,42 \n",
      "2019-01-08  56,09 \n",
      "...            ...\n",
      "2023-07-21  81,99 \n",
      "2023-07-24  83,19 \n",
      "2023-07-25  84,64 \n",
      "2023-07-26  84,82 \n",
      "2023-07-27  84,88 \n",
      "\n",
      "[1161 rows x 1 columns]\n"
     ]
    }
   ],
   "source": [
    "OPEP['FECHA'] = pd.to_datetime(OPEP['FECHA'])\n",
    "OPEP.set_index('FECHA', inplace=True)\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(OPEP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fecha inicial: 2019-01-02 00:00:00\n",
      "Fecha final: 2023-07-27 00:00:00\n",
      "Número de días: 1668\n"
     ]
    }
   ],
   "source": [
    "# Calcular la fecha inicial y fecha final\n",
    "fecha_inicial = OPEP.index.min()\n",
    "fecha_final = OPEP.index.max()\n",
    "\n",
    "# Calcular el número de días entre las fechas\n",
    "num_dias = (fecha_final - fecha_inicial).days + 1\n",
    "\n",
    "# Imprimir los resultados\n",
    "print('Fecha inicial:', fecha_inicial)\n",
    "print('Fecha final:', fecha_final)\n",
    "print('Número de días:', num_dias)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            PRECIO\n",
      "FECHA             \n",
      "2019-01-02  52,14 \n",
      "2019-01-03  52,93 \n",
      "2019-01-04  55,13 \n",
      "2019-01-07  56,42 \n",
      "2019-01-08  56,09 \n",
      "...            ...\n",
      "2023-07-21  81,99 \n",
      "2023-07-24  83,19 \n",
      "2023-07-25  84,64 \n",
      "2023-07-26  84,82 \n",
      "2023-07-27  84,88 \n",
      "\n",
      "[1161 rows x 1 columns]\n"
     ]
    }
   ],
   "source": [
    "# Redefinir el índice con el formato de año-mes-día\n",
    "OPEP.index = OPEP.index.strftime('%Y-%m-%d')\n",
    "\n",
    "# Mostrar el DataFrame actualizado\n",
    "print(OPEP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "object\n"
     ]
    }
   ],
   "source": [
    "print(OPEP['PRECIO'].dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2019-01-02\n"
     ]
    }
   ],
   "source": [
    "fecha_inicial = OPEP.index.min()\n",
    "print(fecha_inicial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convertir los valores de la columna 'PRECIO' a números con coma decimal en lugar de punto decimal\n",
    "OPEP['PRECIO'] = OPEP['PRECIO'].str.replace(',', '.').astype(float)\n",
    "\n",
    "# Cambiar el nombre de la columna 'PRECIO' a 'PRECIO OPEP'\n",
    "OPEP.rename(columns={'PRECIO': 'PRECIO OPEP'}, inplace=True)\n",
    "# Redondear los valores a un decimal\n",
    "OPEP['PRECIO OPEP'] = OPEP['PRECIO OPEP'].round(2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECIO OPEP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1161.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>70.538277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>21.987607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>12.220000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>60.020000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>69.880000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>82.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>128.460000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       PRECIO OPEP\n",
       "count  1161.000000\n",
       "mean     70.538277\n",
       "std      21.987607\n",
       "min      12.220000\n",
       "25%      60.020000\n",
       "50%      69.880000\n",
       "75%      82.300000\n",
       "max     128.460000"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECIO OPEP</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FECHA</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2019-01-02</th>\n",
       "      <td>52.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-03</th>\n",
       "      <td>52.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-04</th>\n",
       "      <td>55.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-07</th>\n",
       "      <td>56.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-08</th>\n",
       "      <td>56.09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            PRECIO OPEP\n",
       "FECHA                  \n",
       "2019-01-02        52.14\n",
       "2019-01-03        52.93\n",
       "2019-01-04        55.13\n",
       "2019-01-07        56.42\n",
       "2019-01-08        56.09"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
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   "source": [
    "# Graficar los datos\n",
    "fig = px.line(OPEP, x=OPEP.index, y='PRECIO OPEP', title='Precio del petróleo OPEP (USD/BBL) a lo largo del tiempo')\n",
    "fig.show()"
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         "text": "Precio del petróleo OPEP (USD/BBL) - 2023"
        },
        "xaxis": {
         "anchor": "y",
         "domain": [
          0,
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          "text": "PRECIO OPEP"
         }
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Redefinir el índice con el formato de año-mes-día\n",
    "OPEP.index = pd.to_datetime(OPEP.index)\n",
    "\n",
    "# Filtrar los datos por año\n",
    "df_2019 = OPEP[OPEP.index.year == 2019]\n",
    "df_2020 = OPEP[OPEP.index.year == 2020]\n",
    "df_2021 = OPEP[OPEP.index.year == 2021]\n",
    "df_2022 = OPEP[OPEP.index.year == 2022]\n",
    "df_2023 = OPEP[OPEP.index.year == 2023]\n",
    "\n",
    "# Crear el gráfico de líneas para cada año\n",
    "fig_2019 = px.line(df_2019, x=df_2019.index, y='PRECIO OPEP', title='Precio del petróleo OPEP (USD/BBL) - 2019')\n",
    "fig_2020 = px.line(df_2020, x=df_2020.index, y='PRECIO OPEP', title='Precio del petróleo OPEP (USD/BBL) - 2020')\n",
    "fig_2021 = px.line(df_2021, x=df_2021.index, y='PRECIO OPEP', title='Precio del petróleo OPEP (USD/BBL) - 2021')\n",
    "fig_2022 = px.line(df_2022, x=df_2022.index, y='PRECIO OPEP', title='Precio del petróleo OPEP (USD/BBL) - 2022')\n",
    "fig_2023 = px.line(df_2023, x=df_2023.index, y='PRECIO OPEP', title='Precio del petróleo OPEP (USD/BBL) - 2023')\n",
    "\n",
    "# Mostrar los gráficos individualmente\n",
    "fig_2019.show()\n",
    "fig_2020.show()\n",
    "fig_2021.show()\n",
    "fig_2022.show()\n",
    "fig_2023.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MODELO SARIMAX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test de estacionariedad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como se puede observar, hay una tendencia en el tiempo y eso sugiere que los datos no son estacionarios. Sin embargo, para asegurar la estacionariedad de la serie, utilizamos el test Dickey-Fuller."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [],
   "source": [
    "OPEP_copia['PRECIO'] = OPEP_copia['PRECIO'].str.replace(',', '.').astype(float)\n",
    "# Establecer la columna 'FECHA' como índice\n",
    "OPEP_copia.set_index('FECHA', inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'adf': -1.5617904178661435,\n",
       " 'pvalue': 0.5027536130313731,\n",
       " 'usedlag': 17,\n",
       " 'nobs': 1143,\n",
       " 'criticalvalues': {'1%': -3.4360840741163168,\n",
       "  '5%': -2.864071964072552,\n",
       "  '10%': -2.568118081861596},\n",
       " 'icbest': 4375.9051048424735}"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_OPEP = adfuller(OPEP_copia['PRECIO'])\n",
    "dict(zip(['adf', 'pvalue', 'usedlag', 'nobs', 'critical' 'values', 'icbest'], result_OPEP))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "        pvalue > 0.05 ---->.  0.50275 > 0.05, NO ES ESTACIONARIO\n",
    "Para corregir la no estacionariedad, necesitamos diferenciar el valor de nuestra serie de tiempo: restar la observación anterior de la observación actual.\n",
    "\n",
    "- diferencia(T) = observación(T) — observación(T-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECIO</th>\n",
       "      <th>OPEP1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FECHA</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2019-01-02</th>\n",
       "      <td>52.14</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-03</th>\n",
       "      <td>52.93</td>\n",
       "      <td>0.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-04</th>\n",
       "      <td>55.13</td>\n",
       "      <td>2.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-07</th>\n",
       "      <td>56.42</td>\n",
       "      <td>1.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-08</th>\n",
       "      <td>56.09</td>\n",
       "      <td>-0.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "            PRECIO  OPEP1\n",
       "FECHA                    \n",
       "2019-01-02   52.14    NaN\n",
       "2019-01-03   52.93   0.79\n",
       "2019-01-04   55.13   2.20\n",
       "2019-01-07   56.42   1.29\n",
       "2019-01-08   56.09  -0.33"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP_copia['OPEP1'] = OPEP_copia['PRECIO'] - OPEP_copia['PRECIO'].shift(1)\n",
    "OPEP_copia.head()"
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   ],
   "source": [
    "px.line(OPEP_copia['OPEP1']) #Valor pasado menos el presente"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'adf': -6.705036630557044,\n",
       " 'pvalue': 3.8040307854707524e-09,\n",
       " 'usedlag': 16,\n",
       " 'nobs': 1143,\n",
       " 'criticalvalues': {'1%': -3.4360840741163168,\n",
       "  '5%': -2.864071964072552,\n",
       "  '10%': -2.568118081861596},\n",
       " 'icbest': 4373.250646343316}"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_OPEP1 = adfuller(OPEP_copia['OPEP1'].dropna())#dropna es para quitar los nulos porque sino no funciona. \n",
    "dict(zip(['adf', 'pvalue', 'usedlag', 'nobs', 'critical' 'values', 'icbest'], result_OPEP1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    pvalue <  0.05 ---->.  3.804 <  0.05,  ES ESTACIONARIO\n",
    "\n",
    "    Para el modelo, utilizamos: \n",
    "\n",
    "        d=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECIO</th>\n",
       "      <th>OPEP1</th>\n",
       "      <th>OPEP12</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FECHA</th>\n",
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       "      <th>2019-01-02</th>\n",
       "      <td>52.14</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-03</th>\n",
       "      <td>52.93</td>\n",
       "      <td>0.79</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-04</th>\n",
       "      <td>55.13</td>\n",
       "      <td>2.20</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-07</th>\n",
       "      <td>56.42</td>\n",
       "      <td>1.29</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>2019-01-08</th>\n",
       "      <td>56.09</td>\n",
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       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2019-01-09</th>\n",
       "      <td>58.22</td>\n",
       "      <td>2.13</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-10</th>\n",
       "      <td>59.46</td>\n",
       "      <td>1.24</td>\n",
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       "      <th>2019-01-11</th>\n",
       "      <td>60.00</td>\n",
       "      <td>0.54</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2019-01-14</th>\n",
       "      <td>58.39</td>\n",
       "      <td>-1.61</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2019-01-15</th>\n",
       "      <td>58.24</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2019-01-16</th>\n",
       "      <td>59.52</td>\n",
       "      <td>1.28</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2019-01-17</th>\n",
       "      <td>59.63</td>\n",
       "      <td>0.11</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2019-01-18</th>\n",
       "      <td>60.90</td>\n",
       "      <td>1.27</td>\n",
       "      <td>8.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-21</th>\n",
       "      <td>61.49</td>\n",
       "      <td>0.59</td>\n",
       "      <td>8.56</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            PRECIO  OPEP1  OPEP12\n",
       "FECHA                            \n",
       "2019-01-02   52.14    NaN     NaN\n",
       "2019-01-03   52.93   0.79     NaN\n",
       "2019-01-04   55.13   2.20     NaN\n",
       "2019-01-07   56.42   1.29     NaN\n",
       "2019-01-08   56.09  -0.33     NaN\n",
       "2019-01-09   58.22   2.13     NaN\n",
       "2019-01-10   59.46   1.24     NaN\n",
       "2019-01-11   60.00   0.54     NaN\n",
       "2019-01-14   58.39  -1.61     NaN\n",
       "2019-01-15   58.24  -0.15     NaN\n",
       "2019-01-16   59.52   1.28     NaN\n",
       "2019-01-17   59.63   0.11     NaN\n",
       "2019-01-18   60.90   1.27    8.76\n",
       "2019-01-21   61.49   0.59    8.56"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP_copia['OPEP12'] = OPEP_copia['PRECIO'] - OPEP_copia['PRECIO'].shift(12)\n",
    "OPEP_copia.head(14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
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           "bgcolor": "#E5ECF6",
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            "linecolor": "white",
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          "title": {
           "x": 0.05
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           "ticks": "",
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         "anchor": "x",
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   ],
   "source": [
    "px.line(OPEP_copia['OPEP12'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'adf': -6.019569775700061,\n",
       " 'pvalue': 1.50501176142666e-07,\n",
       " 'usedlag': 21,\n",
       " 'nobs': 1127,\n",
       " 'criticalvalues': {'1%': -3.4361656672131806,\n",
       "  '5%': -2.864107957764881,\n",
       "  '10%': -2.568137251515397},\n",
       " 'icbest': 4757.084433657213}"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_OPEP12 = adfuller((OPEP_copia['OPEP12']).dropna())\n",
    "dict(zip(['adf', 'pvalue', 'usedlag', 'nobs', 'critical' 'values', 'icbest'], result_OPEP12))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    pvalue <  0.05 ---->.  1.505e-07 <  0.05\n",
    "\n",
    "    Para el modelo, utilizamos: \n",
    "\n",
    "        D=0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test de autocorrelación"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECIO</th>\n",
       "      <th>OPEP1</th>\n",
       "      <th>OPEP12</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FECHA</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2019-01-02</th>\n",
       "      <td>52.14</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-03</th>\n",
       "      <td>52.93</td>\n",
       "      <td>0.79</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-04</th>\n",
       "      <td>55.13</td>\n",
       "      <td>2.20</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-07</th>\n",
       "      <td>56.42</td>\n",
       "      <td>1.29</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-08</th>\n",
       "      <td>56.09</td>\n",
       "      <td>-0.33</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            PRECIO  OPEP1  OPEP12\n",
       "FECHA                            \n",
       "2019-01-02   52.14    NaN     NaN\n",
       "2019-01-03   52.93   0.79     NaN\n",
       "2019-01-04   55.13   2.20     NaN\n",
       "2019-01-07   56.42   1.29     NaN\n",
       "2019-01-08   56.09  -0.33     NaN"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OPEP_copia.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "OPEP1_acf = plot_acf(OPEP_copia['OPEP1'].dropna())\n",
    "OPEP1_pacf = plot_pacf(OPEP_copia['OPEP1'].dropna())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "        No podemos ver cortes claros en ninguno de los gráficos. Sin embargo, hay retrasos significativos en ambos gráficos. Esto sugiere usar un término AR y MA. \n",
    "        \n",
    "        En el modelo experimentemos con:\n",
    "        \n",
    "        p = 1 \n",
    "        q = 1. \n",
    "        \n",
    "    Necesitamos hacer un análisis similar con el componente estacional."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Seasonal componet\n",
    "OPEP12_acf = plot_acf(OPEP_copia['OPEP12'].dropna())\n",
    "OPEP12_pacf = plot_pacf(OPEP_copia['OPEP12'].dropna())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "        En el modelo experimentemos con:\n",
    "        \n",
    "        P = 3 (tiene correlación en un rango de 0-11) \n",
    "        Q = 3 (tiene mas correlacion de 0 a 3) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adjuntamos el precio de WTI como variable exógena "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             FECHA,PRECIO\n",
      "0     2019-01-02,\"52,14 \"\n",
      "1     2019-01-03,\"52,93 \"\n",
      "2     2019-01-04,\"55,13 \"\n",
      "3     2019-01-07,\"56,42 \"\n",
      "4     2019-01-08,\"56,09 \"\n",
      "...                   ...\n",
      "1156  2023-07-21,\"81,99 \"\n",
      "1157  2023-07-24,\"83,19 \"\n",
      "1158  2023-07-25,\"84,64 \"\n",
      "1159  2023-07-26,\"84,82 \"\n",
      "1160  2023-07-27,\"84,88 \"\n",
      "\n",
      "[1161 rows x 1 columns]\n"
     ]
    }
   ],
   "source": [
    "wti = '/Users/leidygarciaguzman/Documents/PRECIO OPEP /DATA/wti.csv'\n",
    "\n",
    "\n",
    "# Leer el archivo CSV utilizando pandas\n",
    "WTI = pd.read_csv(wti, sep=';')\n",
    "\n",
    "# Mostrar el DataFrame para verificar que los datos se han cargado correctamente\n",
    "print(WTI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a range of hyperparameters to test\n",
    "param_dist = {\"order\": [(p, d, q) for p in range(3) for d in [0, 1, 2] for q in range(3)],\n",
    "    \"seasonal_order\": [(P, D, Q, 12) for P in range(3) for D in [0, 1, 2] for Q in range(3)]}\n",
    "\n",
    "\n",
    "# Initialize a random parameter sampler\n",
    "param_list = list(ParameterSampler(param_dist, n_iter=50))\n",
    "\n",
    "\n",
    "# Define Time Series cross-validator\n",
    "tscv = TimeSeriesSplit(n_splits=4)\n",
    "\n",
    "\n",
    "best_aic = np.inf\n",
    "best_bic = np.inf\n",
    "best_params = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.36469D-01    |proj g|=  9.19874D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate    5    f= -7.82613D+00    |proj g|=  1.25886D+04\n",
      "  ys=-1.584E+00  -gs= 6.584E-01 BFGS update SKIPPED\n",
      "  ys=-1.114E-01  -gs= 6.798E-01 BFGS update SKIPPED\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      8    105      2     2     0   9.287D+04  -9.084D+00\n",
      "  F =  -9.0841870307908970     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.00719D+01    |proj g|=  2.17711D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      3     74      2     0     0   1.870D+05  -1.008D+01\n",
      "  F =  -10.075700065142469     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -2.78923D-01    |proj g|=  3.18753D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate    5    f= -6.87954D+00    |proj g|=  1.98322D+04\n",
      "\n",
      "At iterate   10    f= -7.50682D+00    |proj g|=  4.25059D+03\n",
      "\n",
      "At iterate   15    f= -8.63304D+00    |proj g|=  3.47520D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7     18     82      2     0     0   1.184D+09  -9.783D+00\n",
      "  F =  -9.7829211318014373     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.03327D+01    |proj g|=  2.77029D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      4     84      2     0     0   2.372D+05  -1.034D+01\n",
      "  F =  -10.335971981794524     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.71976D-01    |proj g|=  1.54963D+05\n",
      "  ys=-1.366E-15  -gs= 5.008E-12 BFGS update SKIPPED\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      3     64      2     1     0   1.106D+05  -2.006D-01\n",
      "  F = -0.20057867093376011     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -7.51603D-02    |proj g|=  8.00581D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate    5    f= -7.68846D+00    |proj g|=  7.88959D+03\n",
      "\n",
      "At iterate   10    f= -7.90232D+00    |proj g|=  1.74169D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3     12     74      2     0     0   1.642D+04  -8.397D+00\n",
      "  F =  -8.3968580821935568     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -5.84519D-03    |proj g|=  3.15672D+03\n",
      "\n",
      "At iterate    5    f= -1.72892D+00    |proj g|=  7.80584D+01\n",
      "  ys=-7.690E+00  -gs= 9.412E-01 BFGS update SKIPPED\n",
      "\n",
      "At iterate   10    f= -5.89173D+00    |proj g|=  1.00374D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Nonpositive definiteness in Cholesky factorization in formt;\n",
      "   refresh the lbfgs memory and restart the iteration.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate   15    f= -7.66106D+00    |proj g|=  2.82217D+04\n",
      "\n",
      "At iterate   20    f= -8.10305D+00    |proj g|=  1.01609D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3     24    139      3     1     0   1.138D+04  -8.142D+00\n",
      "  F =  -8.1418247920486717     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -3.52733D-02    |proj g|=  5.32424D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate    5    f= -5.60391D-02    |proj g|=  7.44797D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      6     67      2     0     0   7.448D+04  -5.604D-02\n",
      "  F =  -5.6039118164493210E-002\n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            8     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -9.48100D+00    |proj g|=  1.24259D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate    5    f= -9.48114D+00    |proj g|=  1.22412D+06\n",
      "\n",
      "At iterate   10    f= -9.48124D+00    |proj g|=  1.21269D+06\n",
      "\n",
      "At iterate   15    f= -9.48133D+00    |proj g|=  1.20532D+06\n",
      "\n",
      "At iterate   20    f= -9.48140D+00    |proj g|=  1.20186D+06\n",
      "\n",
      "At iterate   25    f= -9.48142D+00    |proj g|=  1.20118D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    8     28    349      1     0     0   1.201D+06  -9.481D+00\n",
      "  F =  -9.4814198360167712     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            8     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.00174D+01    |proj g|=  3.17118D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    8      2     31      1     0     0   2.749D+05  -1.003D+01\n",
      "  F =  -10.028711956945543     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            8     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.02246D+01    |proj g|=  2.48931D+05\n",
      "  ys=-1.559E-01  -gs= 6.969E-02 BFGS update SKIPPED\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    8      4     70      2     1     0   2.232D+05  -1.025D+01\n",
      "  F =  -10.254477041024073     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            8     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.03148D+01    |proj g|=  2.71617D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    8      1     21      1     0     0   2.716D+06  -1.031D+01\n",
      "  F =  -10.314841040189124     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05940D+01    |proj g|=  2.04524D+08\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      1     21      1     0     0   2.045D+08  -1.059D+01\n",
      "  F =  -10.593986931765556     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05940D+01    |proj g|=  1.55244D+08\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      1     21      1     0     0   1.552D+08  -1.059D+01\n",
      "  F =  -10.593986931765556     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05937D+01    |proj g|=  1.50899D+08\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      1     21      1     0     0   1.509D+08  -1.059D+01\n",
      "  F =  -10.593668393960588     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05940D+01    |proj g|=  2.70735D+08\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      1     21      1     0     0   2.707D+08  -1.059D+01\n",
      "  F =  -10.593966840029477     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -9.48100D+00    |proj g|=  1.24259D+06\n",
      "\n",
      "At iterate    5    f= -9.48114D+00    |proj g|=  1.22412D+06\n",
      "\n",
      "At iterate   10    f= -9.48124D+00    |proj g|=  1.21269D+06\n",
      "\n",
      "At iterate   15    f= -9.48133D+00    |proj g|=  1.20532D+06\n",
      "\n",
      "At iterate   20    f= -9.48140D+00    |proj g|=  1.20186D+06\n",
      "\n",
      "At iterate   25    f= -9.48142D+00    |proj g|=  1.20118D+06\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7     28    346      1     0     0   1.201D+06  -9.481D+00\n",
      "  F =  -9.4814198609800666     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.18468D-01    |proj g|=  9.25494D+05\n",
      "\n",
      "At iterate    5    f= -4.45998D+00    |proj g|=  2.62788D+02\n",
      "\n",
      "At iterate   10    f= -6.23896D+00    |proj g|=  1.02892D+04\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7     13     57      1     0     0   4.777D+04  -7.513D+00\n",
      "  F =  -7.5134629556684569     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -8.30931D-02    |proj g|=  6.95026D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate    5    f= -4.44187D+00    |proj g|=  2.41491D+02\n",
      "\n",
      "At iterate   10    f= -5.02304D+00    |proj g|=  4.86877D+03\n",
      "  ys=-4.628E+01  -gs= 6.083E-01 BFGS update SKIPPED\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7     15     82      2     1     0   1.082D+05  -8.078D+00\n",
      "  F =  -8.0782203714491665     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.03148D+01    |proj g|=  2.71617D+06\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      1     21      1     0     0   2.716D+06  -1.031D+01\n",
      "  F =  -10.314841040189124     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -9.48100D+00    |proj g|=  1.24259D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate    5    f= -9.48114D+00    |proj g|=  1.22412D+06\n",
      "\n",
      "At iterate   10    f= -9.48124D+00    |proj g|=  1.21269D+06\n",
      "\n",
      "At iterate   15    f= -9.48133D+00    |proj g|=  1.20532D+06\n",
      "\n",
      "At iterate   20    f= -9.48140D+00    |proj g|=  1.20186D+06\n",
      "\n",
      "At iterate   25    f= -9.48142D+00    |proj g|=  1.20118D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6     28    348      1     0     0   1.201D+06  -9.481D+00\n",
      "  F =  -9.4814198591199421     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.00418D+01    |proj g|=  2.77690D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      1     21      1     0     0   2.777D+05  -1.004D+01\n",
      "  F =  -10.041829923616044     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.02264D+01    |proj g|=  2.37045D+05\n",
      "  ys=-4.805E-01  -gs= 5.619E-02 BFGS update SKIPPED\n",
      "\n",
      "At iterate    5    f= -1.02489D+01    |proj g|=  1.41121D+06\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      6     77      1     1     0   1.411D+06  -1.025D+01\n",
      "  F =  -10.248931111680603     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.03148D+01    |proj g|=  2.71617D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      1     21      1     0     0   2.716D+06  -1.031D+01\n",
      "  F =  -10.314841040189124     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05019D+01    |proj g|=  6.87157D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      1     21      1     0     0   6.872D+04  -1.050D+01\n",
      "  F =  -10.501913939228066     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -3.61881D-02    |proj g|=  9.82169D+05\n",
      "  ys=-2.231E+00  -gs= 7.886E-01 BFGS update SKIPPED\n",
      "\n",
      "At iterate    5    f= -7.73231D+00    |proj g|=  5.63231D+03\n",
      "\n",
      "At iterate   10    f= -8.62900D+00    |proj g|=  6.06502D+04\n",
      "  ys=-4.605E+01  -gs= 6.664E-01 BFGS update SKIPPED\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7     12    107      2     2     0   1.139D+06  -1.002D+01\n",
      "  F =  -10.020234565821104     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05630D+01    |proj g|=  1.40279D+05\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      4     54      1     0     0   1.038D+05  -1.064D+01\n",
      "  F =  -10.636612644773733     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05712D+01    |proj g|=  1.60316D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n",
      " This problem is unconstrained.\n",
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      4     88      2     0     0   1.202D+05  -1.062D+01\n",
      "  F =  -10.622862152232640     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            5     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05031D+01    |proj g|=  6.43543D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n",
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    5      2     60      2     0     0   7.359D+04  -1.084D+01\n",
      "  F =  -10.842701932774727     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            5     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05484D+01    |proj g|=  9.03226D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    5      3     44      1     0     0   6.319D+04  -1.068D+01\n",
      "  F =  -10.677520992559712     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            5     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05634D+01    |proj g|=  7.85403D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    5      2     59      2     0     0   5.526D+04  -1.060D+01\n",
      "  F =  -10.596541441634477     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            5     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05710D+01    |proj g|=  1.38921D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    5      4     76      2     0     0   1.022D+05  -1.065D+01\n",
      "  F =  -10.645493227020269     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05013D+01    |proj g|=  6.86640D+04\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      1     21      1     0     0   6.866D+04  -1.050D+01\n",
      "  F =  -10.501264876220493     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -3.89979D-02    |proj g|=  9.81880D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      4     75      2     0     0   9.465D+05  -9.504D+00\n",
      "  F =  -9.5037054302624338     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05630D+01    |proj g|=  1.40279D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      4     54      1     0     0   1.038D+05  -1.064D+01\n",
      "  F =  -10.636612644716381     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            6     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05711D+01    |proj g|=  1.84023D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n",
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    6      5     86      2     0     0   1.329D+05  -1.059D+01\n",
      "  F =  -10.587415509790668     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            8     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -0.00000D+00    |proj g|=  1.08557D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  ys=-5.531E+01  -gs= 3.906E-01 BFGS update SKIPPED\n",
      "\n",
      "At iterate    5    f= -9.08778D+00    |proj g|=  3.07968D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    8      7     71      1     1     0   3.115D+04  -9.089D+00\n",
      "  F =  -9.0891357721587784     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            8     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.67664D-02    |proj g|=  9.58394D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  ys=-3.414E+01  -gs= 9.848E-01 BFGS update SKIPPED\n",
      "\n",
      "At iterate    5    f= -8.59632D+00    |proj g|=  3.28464D+04\n",
      "\n",
      "At iterate   10    f= -8.82285D+00    |proj g|=  3.00702D+07\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    8     12     76      1     1     0   1.772D+06  -8.825D+00\n",
      "  F =  -8.8246641988690211     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            8     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.11856D-02    |proj g|=  9.68942D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  ys=-2.830E+01  -gs= 9.928E-01 BFGS update SKIPPED\n",
      "  ys=-1.685E-07  -gs= 3.569E-05 BFGS update SKIPPED\n",
      "\n",
      "At iterate    5    f= -8.54919D+00    |proj g|=  1.64280D+04\n",
      "  ys=-8.520E-11  -gs= 4.546E-08 BFGS update SKIPPED\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    8      6     73      2     3     0   1.643D+04  -8.549D+00\n",
      "  F =  -8.5491873691591547     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            8     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -0.00000D+00    |proj g|=  9.74564D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate    5    f= -8.93846D+00    |proj g|=  1.01866D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    8      7     87      2     0     0   1.599D+06  -9.170D+00\n",
      "  F =  -9.1697387584568180     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            5     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -0.00000D+00    |proj g|=  9.29688D+05\n",
      "  ys=-1.541E-03  -gs= 3.576E-02 BFGS update SKIPPED\n",
      "\n",
      "At iterate    5    f= -8.94332D+00    |proj g|=  2.61384D+04\n",
      "  ys=-4.493E-04  -gs= 2.701E-02 BFGS update SKIPPED\n",
      "  ys=-1.036E-04  -gs= 5.649E-03 BFGS update SKIPPED\n",
      "  ys=-4.301E+01  -gs= 1.341E+00 BFGS update SKIPPED\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    5      9    105      2     4     0   9.238D+05  -9.238D+00\n",
      "  F =  -9.2376170135499756     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            5     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.67664D-02    |proj g|=  9.58394D+05\n",
      "  ys=-3.414E+01  -gs= 9.848E-01 BFGS update SKIPPED\n",
      "\n",
      "At iterate    5    f= -8.62640D+00    |proj g|=  4.63784D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    5      8     73      2     1     0   1.811D+04  -8.963D+00\n",
      "  F =  -8.9628939719742835     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            5     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.11856D-02    |proj g|=  9.68942D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  ys=-2.640E+01  -gs= 9.929E-01 BFGS update SKIPPED\n",
      "  ys=-1.087E-07  -gs= 9.492E-06 BFGS update SKIPPED\n",
      "\n",
      "At iterate    5    f= -8.55222D+00    |proj g|=  1.63989D+04\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    5      7     54      1     2     0   1.640D+04  -8.552D+00\n",
      "  F =  -8.5522393604813374     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            5     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -0.00000D+00    |proj g|=  2.85911D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "At iterate    5    f= -9.15653D+00    |proj g|=  1.02948D+06\n",
      "\n",
      "At iterate   10    f= -9.25378D+00    |proj g|=  3.13664D+04\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    5     12     86      1     0     0   3.019D+04  -9.254D+00\n",
      "  F =  -9.2537893245238649     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05031D+01    |proj g|=  6.43543D+04\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      2     60      2     0     0   7.359D+04  -1.084D+01\n",
      "  F =  -10.842701932774727     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05484D+01    |proj g|=  9.03226D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n",
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n",
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      3     44      1     0     0   6.319D+04  -1.068D+01\n",
      "  F =  -10.677520992561087     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05634D+01    |proj g|=  7.86997D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      2     59      2     0     0   5.507D+04  -1.059D+01\n",
      "  F =  -10.594194237862348     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05711D+01    |proj g|=  1.39750D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      4     79      2     0     0   1.024D+05  -1.064D+01\n",
      "  F =  -10.642823858593687     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05012D+01    |proj g|=  7.97118D+04\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      2     61      2     0     0   6.751D+04  -1.058D+01\n",
      "  F =  -10.583854297214979     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05475D+01    |proj g|=  1.58156D+05\n",
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      4     50      1     0     0   1.172D+05  -1.060D+01\n",
      "  F =  -10.598792668237257     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05630D+01    |proj g|=  1.40279D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n",
      " This problem is unconstrained.\n",
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      4     55      1     0     0   1.038D+05  -1.064D+01\n",
      "  F =  -10.636612644696022     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            3     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.05707D+01    |proj g|=  2.48210D+05\n",
      "\n",
      "At iterate    5    f= -1.05808D+01    |proj g|=  1.98231D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    3      6     68      1     0     0   1.982D+05  -1.058D+01\n",
      "  F =  -10.580836979358617     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -9.48100D+00    |proj g|=  1.24259D+06\n",
      "\n",
      "At iterate    5    f= -9.48114D+00    |proj g|=  1.22412D+06\n",
      "\n",
      "At iterate   10    f= -9.48124D+00    |proj g|=  1.21269D+06\n",
      "\n",
      "At iterate   15    f= -9.48133D+00    |proj g|=  1.20532D+06\n",
      "\n",
      "At iterate   20    f= -9.48140D+00    |proj g|=  1.20186D+06\n",
      "\n",
      "At iterate   25    f= -9.48142D+00    |proj g|=  1.20118D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n",
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7     28    370      2     0     0   1.201D+06  -9.481D+00\n",
      "  F =  -9.4814198367507831     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n",
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.00399D+01    |proj g|=  6.84776D+05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n",
      "\n",
      " Bad direction in the line search;\n",
      "   refresh the lbfgs memory and restart the iteration.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      3     57      2     0     0   2.891D+05  -1.010D+01\n",
      "  F =  -10.104509970977318     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n",
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.02240D+01    |proj g|=  7.84721D+05\n",
      "\n",
      "At iterate    5    f= -1.02572D+01    |proj g|=  5.45867D+05\n",
      "  ys=-8.870E-03  -gs= 8.065E-03 BFGS update SKIPPED\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Warning:  more than 10 function and gradient\n",
      "   evaluations in the last line search.  Termination\n",
      "   may possibly be caused by a bad search direction.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      7     73      1     1     0   2.257D+05  -1.026D+01\n",
      "  F =  -10.259500257581694     \n",
      "\n",
      "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH             \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " This problem is unconstrained.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RUNNING THE L-BFGS-B CODE\n",
      "\n",
      "           * * *\n",
      "\n",
      "Machine precision = 2.220D-16\n",
      " N =            7     M =           10\n",
      "\n",
      "At X0         0 variables are exactly at the bounds\n",
      "\n",
      "At iterate    0    f= -1.03148D+01    |proj g|=  2.71617D+06\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      " Line search cannot locate an adequate point after MAXLS\n",
      "  function and gradient evaluations.\n",
      "  Previous x, f and g restored.\n",
      " Possible causes: 1 error in function or gradient evaluation;\n",
      "                  2 rounding error dominate computation.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "           * * *\n",
      "\n",
      "Tit   = total number of iterations\n",
      "Tnf   = total number of function evaluations\n",
      "Tnint = total number of segments explored during Cauchy searches\n",
      "Skip  = number of BFGS updates skipped\n",
      "Nact  = number of active bounds at final generalized Cauchy point\n",
      "Projg = norm of the final projected gradient\n",
      "F     = final function value\n",
      "\n",
      "           * * *\n",
      "\n",
      "   N    Tit     Tnf  Tnint  Skip  Nact     Projg        F\n",
      "    7      1     21      1     0     0   2.716D+06  -1.031D+01\n",
      "  F =  -10.314841040189124     \n",
      "\n",
      "ABNORMAL_TERMINATION_IN_LNSRCH                              \n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/rl/7bt84j4j31gg1ssp767d9xgm0000gn/T/ipykernel_22237/546618891.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     15\u001b[0m         sarima = SARIMAX(cv_train['PRECIO OPEP'], exog=cv_train['PRECIO OPEP'],\n\u001b[1;32m     16\u001b[0m                          order=params['order'], seasonal_order=params['seasonal_order'])\n\u001b[0;32m---> 17\u001b[0;31m         \u001b[0msarima_results\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msarima\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m         \u001b[0;31m# Save AIC and BIC scores\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, start_params, transformed, includes_fixed, cov_type, cov_kwds, method, maxiter, full_output, disp, callback, return_params, optim_score, optim_complex_step, optim_hessian, flags, low_memory, **kwargs)\u001b[0m\n\u001b[1;32m    726\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    727\u001b[0m                 \u001b[0mfunc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msmooth\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 728\u001b[0;31m             res = func(mlefit.params, transformed=False, includes_fixed=False,\n\u001b[0m\u001b[1;32m    729\u001b[0m                        cov_type=cov_type, cov_kwds=cov_kwds)\n\u001b[1;32m    730\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36msmooth\u001b[0;34m(self, params, transformed, includes_fixed, complex_step, cov_type, cov_kwds, return_ssm, results_class, results_wrapper_class, **kwargs)\u001b[0m\n\u001b[1;32m    887\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    888\u001b[0m         \u001b[0;31m# Wrap in a results object\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 889\u001b[0;31m         return self._wrap_results(params, result, return_ssm, cov_type,\n\u001b[0m\u001b[1;32m    890\u001b[0m                                   \u001b[0mcov_kwds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresults_class\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    891\u001b[0m                                   results_wrapper_class)\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36m_wrap_results\u001b[0;34m(self, params, result, return_raw, cov_type, cov_kwds, results_class, wrapper_class)\u001b[0m\n\u001b[1;32m    786\u001b[0m                 \u001b[0mwrapper_class\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_res_classes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'fit'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    787\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 788\u001b[0;31m             \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mresults_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mresult_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    789\u001b[0m             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwrapper_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    790\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/sarimax.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, model, params, filter_results, cov_type, **kwargs)\u001b[0m\n\u001b[1;32m   1804\u001b[0m     def __init__(self, model, params, filter_results, cov_type=None,\n\u001b[1;32m   1805\u001b[0m                  **kwargs):\n\u001b[0;32m-> 1806\u001b[0;31m         super(SARIMAXResults, self).__init__(model, params, filter_results,\n\u001b[0m\u001b[1;32m   1807\u001b[0m                                              cov_type, **kwargs)\n\u001b[1;32m   1808\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, model, params, results, cov_type, cov_kwds, **kwargs)\u001b[0m\n\u001b[1;32m   2335\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2336\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_rank\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2337\u001b[0;31m             self._get_robustcov_results(cov_type=cov_type, use_self=True,\n\u001b[0m\u001b[1;32m   2338\u001b[0m                                         **cov_kwds)\n\u001b[1;32m   2339\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLinAlgError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36m_get_robustcov_results\u001b[0;34m(self, cov_type, **kwargs)\u001b[0m\n\u001b[1;32m   2565\u001b[0m                                                 approx_type=approx_type_str)\n\u001b[1;32m   2566\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcov_type\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'opg'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2567\u001b[0;31m             \u001b[0mres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcov_params_default\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcov_params_opg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2568\u001b[0m             res.cov_kwds['description'] = descriptions['OPG'].format(\n\u001b[1;32m   2569\u001b[0m                                                 approx_type=approx_type_str)\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/pandas/_libs/properties.pyx\u001b[0m in \u001b[0;36mpandas._libs.properties.CachedProperty.__get__\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36mcov_params_opg\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   2695\u001b[0m         \u001b[0mproduct\u001b[0m \u001b[0mof\u001b[0m \u001b[0mgradients\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2696\u001b[0m         \"\"\"\n\u001b[0;32m-> 2697\u001b[0;31m         return self._cov_params_opg(self._cov_approx_complex_step,\n\u001b[0m\u001b[1;32m   2698\u001b[0m                                     self._cov_approx_centered)\n\u001b[1;32m   2699\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36m_cov_params_opg\u001b[0;34m(self, approx_complex_step, approx_centered)\u001b[0m\n\u001b[1;32m   2662\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2663\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_cov_params_opg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mapprox_complex_step\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mapprox_centered\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2664\u001b[0;31m         evaluated_hessian = self.nobs_effective * self.model._hessian_opg(\n\u001b[0m\u001b[1;32m   2665\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtransformed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mincludes_fixed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2666\u001b[0m             \u001b[0mapprox_complex_step\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mapprox_complex_step\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36m_hessian_opg\u001b[0;34m(self, params, **kwargs)\u001b[0m\n\u001b[1;32m   1540\u001b[0m         \u001b[0minformation\u001b[0m \u001b[0mmatrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1541\u001b[0m         \"\"\"\n\u001b[0;32m-> 1542\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mopg_information_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1543\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1544\u001b[0m     def _hessian_finite_difference(self, params, approx_centered=False,\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36mopg_information_matrix\u001b[0;34m(self, params, transformed, includes_fixed, approx_complex_step, **kwargs)\u001b[0m\n\u001b[1;32m   1227\u001b[0m                              \" with untransformed parameters.\")\n\u001b[1;32m   1228\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1229\u001b[0;31m         score_obs = self.score_obs(params, transformed=transformed,\n\u001b[0m\u001b[1;32m   1230\u001b[0m                                    \u001b[0mincludes_fixed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mincludes_fixed\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1231\u001b[0m                                    \u001b[0mapprox_complex_step\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mapprox_complex_step\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36mscore_obs\u001b[0;34m(self, params, method, transformed, includes_fixed, approx_complex_step, approx_centered, **kwargs)\u001b[0m\n\u001b[1;32m   1446\u001b[0m             \u001b[0mepsilon\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_get_epsilon\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2.\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1447\u001b[0m             \u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'complex_step'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1448\u001b[0;31m             score = approx_fprime_cs(params, self.loglikeobs, epsilon=epsilon,\n\u001b[0m\u001b[1;32m   1449\u001b[0m                                      kwargs=kwargs)\n\u001b[1;32m   1450\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mmethod\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'approx'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tools/numdiff.py\u001b[0m in \u001b[0;36mapprox_fprime_cs\u001b[0;34m(x, f, epsilon, args, kwargs)\u001b[0m\n\u001b[1;32m    246\u001b[0m     \u001b[0mincrements\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0midentity\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;36m1j\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    247\u001b[0m     \u001b[0;31m# TODO: see if this can be vectorized, but usually dim is small\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 248\u001b[0;31m     partials = [f(x+ih, *args, **kwargs).imag / epsilon[i]\n\u001b[0m\u001b[1;32m    249\u001b[0m                 for i, ih in enumerate(increments)]\n\u001b[1;32m    250\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tools/numdiff.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m    246\u001b[0m     \u001b[0mincrements\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0midentity\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;36m1j\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    247\u001b[0m     \u001b[0;31m# TODO: see if this can be vectorized, but usually dim is small\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 248\u001b[0;31m     partials = [f(x+ih, *args, **kwargs).imag / epsilon[i]\n\u001b[0m\u001b[1;32m    249\u001b[0m                 for i, ih in enumerate(increments)]\n\u001b[1;32m    250\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py\u001b[0m in \u001b[0;36mloglikeobs\u001b[0;34m(self, params, transformed, includes_fixed, complex_step, **kwargs)\u001b[0m\n\u001b[1;32m    986\u001b[0m                     complex_step=complex_step)\n\u001b[1;32m    987\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 988\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mssm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloglikeobs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcomplex_step\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcomplex_step\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    989\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    990\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0msimulation_smoother\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msimulation_output\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/kalman_filter.py\u001b[0m in \u001b[0;36mloglikeobs\u001b[0;34m(self, **kwargs)\u001b[0m\n\u001b[1;32m   1048\u001b[0m                 \u001b[0;34m'conserve_memory'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1049\u001b[0m                 MEMORY_CONSERVE ^ (MEMORY_NO_FORECAST | MEMORY_NO_LIKELIHOOD))\n\u001b[0;32m-> 1050\u001b[0;31m         \u001b[0mkfilter\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_filter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1051\u001b[0m         \u001b[0mllf_obs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkfilter\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloglikelihood\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1052\u001b[0m         loglikelihood_burn = kwargs.get('loglikelihood_burn',\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/kalman_filter.py\u001b[0m in \u001b[0;36m_filter\u001b[0;34m(self, filter_method, inversion_method, stability_method, conserve_memory, filter_timing, tolerance, loglikelihood_burn, complex_step)\u001b[0m\n\u001b[1;32m    904\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    905\u001b[0m         \u001b[0;31m# Run the filter\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 906\u001b[0;31m         \u001b[0mkfilter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    907\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    908\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mkfilter\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# Cross-validation and hyperparameter tuning\n",
    "for params in param_list:\n",
    "    aic_scores = []\n",
    "    bic_scores = []\n",
    "\n",
    "    # Cross-validation loop\n",
    "    for train_index, test_index in tscv.split(OPEP):\n",
    "        train_index_list = list(train_index)\n",
    "        test_index_list = list(test_index)\n",
    "\n",
    "        cv_train = OPEP.iloc[train_index_list]\n",
    "        cv_test = OPEP.iloc[test_index_list]\n",
    "\n",
    "        # Fit SARIMAX model\n",
    "        sarima = SARIMAX(cv_train['PRECIO OPEP'], exog=cv_train['PRECIO OPEP'],\n",
    "                         order=params['order'], seasonal_order=params['seasonal_order'])\n",
    "        sarima_results = sarima.fit()\n",
    "\n",
    "        # Save AIC and BIC scores\n",
    "        aic_scores.append(sarima_results.aic)\n",
    "        bic_scores.append(sarima_results.bic)\n",
    "\n",
    "    # Average AIC and BIC scores\n",
    "    mean_aic = np.mean(aic_scores)\n",
    "    mean_bic = np.mean(bic_scores)\n",
    "\n",
    "    # Update best parameters if current model has a lower AIC and BIC\n",
    "    if mean_aic < best_aic and mean_bic < best_bic:\n",
    "        best_aic = mean_aic\n",
    "        best_bic = mean_bic\n",
    "        best_params = params\n",
    "\n",
    "# Print the best parameters and the corresponding AIC and BIC\n",
    "print('Best parameters:', best_params)\n",
    "print('Best AIC:', best_aic)\n",
    "print('Best BIC:', best_bic)\n",
    "\n",
    "# Fit the best model\n",
    "best_model = SARIMAX(OPEP['PRECIO OPEP'], exog=OPEP['PRECIO OPEP'],\n",
    "                     order=best_params['order'], seasonal_order=best_params['seasonal_order'])\n",
    "best_model_fit = best_model.fit()\n",
    "\n",
    "\n",
    "# Define future US Dollar Index\n",
    "future_WTI_price = [101.64, 103.06, 103.66, 104.33, 103.57, 102.59, 99.42, 99.48, 101.97, 102.85, 103.33, 102.4, \n",
    "                          101.23, 100.08, 99.78, 98.72, 97.62, 98.34]\n",
    "\n",
    "\n",
    "# Create forecast object\n",
    "forecast_object = best_model_fit.get_forecast(steps=18, exog=np.array(future_WTI_price).reshape(-1, 1),alpha=0.2)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Extract prediction mean\n",
    "mean = forecast_object.predicted_mean\n",
    "\n",
    "\n",
    "# Extract the forecast dates\n",
    "datescf = pd.date_range(start=df.index[-1], periods=18, freq='MS')\n",
    "\n",
    "\n",
    "# Predictions on historical data\n",
    "in_sample_forecast = best_model_fit.get_prediction(start=pd.to_datetime('2019-01-02'), \n",
    "                                                   end=df.index[-1], \n",
    "                                                   dynamic=False, \n",
    "                                                   exog=df['PRECIO OPEP'][df.index >= pd.to_datetime('2019-01-02')])\n",
    "\n",
    "\n",
    "in_sample_mean = in_sample_forecast.predicted_mean\n",
    "\n",
    "\n",
    "# Replace negative predicted values with 0\n",
    "in_sample_mean[in_sample_mean < 0] = 0\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Confidence intervals for the in-sample data\n",
    "in_sample_conf_int = in_sample_forecast.conf_int()\n",
    "\n",
    "\n",
    "# Correct any negative lower confidence levels in the in-sample data\n",
    "in_sample_conf_int[in_sample_conf_int.iloc[:, 0] < 0] = 0\n",
    "\n",
    "\n",
    "# Confidence intervals for the out-of-sample data\n",
    "conf_int = best_model_fit.get_forecast(steps=len(future_WTI_price), exog=future_WTI_price).conf_int()\n",
    "\n",
    "\n",
    "# Correct any negative lower confidence levels in the out-of-sample data\n",
    "conf_int[conf_int.iloc[:, 0] < 0] = 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'list' object has no attribute 'iloc'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/rl/7bt84j4j31gg1ssp767d9xgm0000gn/T/ipykernel_16113/495265113.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     25\u001b[0m     \u001b[0;31m# Cross-validation loop\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mtrain_index\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtest_index\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtscv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 27\u001b[0;31m         \u001b[0mcv_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcv_test\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtrain_index\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtest_index\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     28\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     29\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'list' object has no attribute 'iloc'"
     ]
    }
   ],
   "source": [
    "# Define a range of hyperparameters to test\n",
    "param_dist = {\"order\": [(p, d, q) for p in range(3) for d in [0, 1, 2] for q in range(3)],\n",
    "    \"seasonal_order\": [(P, D, Q, 12) for P in range(3) for D in [0, 1, 2] for Q in range(3)]}\n",
    "\n",
    "\n",
    "# Initialize a random parameter sampler\n",
    "param_list = list(ParameterSampler(param_dist, n_iter=50))\n",
    "\n",
    "\n",
    "# Define Time Series cross-validator\n",
    "tscv = TimeSeriesSplit(n_splits=4)\n",
    "\n",
    "\n",
    "best_aic = np.inf\n",
    "best_bic = np.inf\n",
    "best_params = None\n",
    "\n",
    "\n",
    "# Cross-validation and hyperparameter tuning\n",
    "for params in param_list:\n",
    "    aic_scores = []\n",
    "    bic_scores = []\n",
    "\n",
    "\n",
    "    # Cross-validation loop\n",
    "    for train_index, test_index in tscv.split(OPEP):\n",
    "        cv_train, cv_test = OPEP.iloc[train_index], OPEP.iloc[test_index]\n",
    "\n",
    "\n",
    "        # Fit SARIMAX model\n",
    "        sarima = SARIMAX(cv_train['PRECIO OPEP'], exog=cv_train['PRECIO OPEP'],\n",
    "                         order=params['order'], seasonal_order=params['seasonal_order'])\n",
    "        sarima_results = sarima.fit()\n",
    "\n",
    "\n",
    "        # Save AIC and BIC scores\n",
    "        aic_scores.append(sarima_results.aic)\n",
    "        bic_scores.append(sarima_results.bic)\n",
    "\n",
    "\n",
    "    # Average AIC and BIC scores\n",
    "    mean_aic = np.mean(aic_scores)\n",
    "    mean_bic = np.mean(bic_scores)\n",
    "\n",
    "\n",
    "    # Update best parameters if current model has a lower AIC and BIC\n",
    "    if mean_aic < best_aic and mean_bic < best_bic:\n",
    "        best_aic = mean_aic\n",
    "        best_bic = mean_bic\n",
    "        best_params = params\n",
    "\n",
    "\n",
    "# Print the best parameters and the corresponding AIC and BIC\n",
    "print('Best parameters:', best_params)\n",
    "print('Best AIC:', best_aic)\n",
    "print('Best BIC:', best_bic)\n",
    "\n",
    "\n",
    "# Fit the best model\n",
    "best_model = SARIMAX(OPEP['PRECIO OPEP'], exog=OPEP['PRECIO OPEP'],\n",
    "                     order=best_params['order'], seasonal_order=best_params['seasonal_order'])\n",
    "best_model_fit = best_model.fit()\n",
    "\n",
    "\n",
    "# Define future US Dollar Index\n",
    "future_WTI_price = [101.64, 103.06, 103.66, 104.33, 103.57, 102.59, 99.42, 99.48, 101.97, 102.85, 103.33, 102.4, \n",
    "                          101.23, 100.08, 99.78, 98.72, 97.62, 98.34]\n",
    "\n",
    "\n",
    "# Create forecast object\n",
    "forecast_object = best_model_fit.get_forecast(steps=18, exog=np.array(future_WTI_price).reshape(-1, 1),alpha=0.2)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Extract prediction mean\n",
    "mean = forecast_object.predicted_mean\n",
    "\n",
    "\n",
    "# Extract the forecast dates\n",
    "datescf = pd.date_range(start=df.index[-1], periods=18, freq='MS')\n",
    "\n",
    "\n",
    "# Predictions on historical data\n",
    "in_sample_forecast = best_model_fit.get_prediction(start=pd.to_datetime('2019-01-02'), \n",
    "                                                   end=df.index[-1], \n",
    "                                                   dynamic=False, \n",
    "                                                   exog=df['PRECIO OPEP'][df.index >= pd.to_datetime('2019-01-02')])\n",
    "\n",
    "\n",
    "in_sample_mean = in_sample_forecast.predicted_mean\n",
    "\n",
    "\n",
    "# Replace negative predicted values with 0\n",
    "in_sample_mean[in_sample_mean < 0] = 0\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Confidence intervals for the in-sample data\n",
    "in_sample_conf_int = in_sample_forecast.conf_int()\n",
    "\n",
    "\n",
    "# Correct any negative lower confidence levels in the in-sample data\n",
    "in_sample_conf_int[in_sample_conf_int.iloc[:, 0] < 0] = 0\n",
    "\n",
    "\n",
    "# Confidence intervals for the out-of-sample data\n",
    "conf_int = best_model_fit.get_forecast(steps=len(future_WTI_price), exog=future_WTI_price).conf_int()\n",
    "\n",
    "\n",
    "# Correct any negative lower confidence levels in the out-of-sample data\n",
    "conf_int[conf_int.iloc[:, 0] < 0] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'list' object has no attribute 'iloc'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/rl/7bt84j4j31gg1ssp767d9xgm0000gn/T/ipykernel_17915/2862171096.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     20\u001b[0m     \u001b[0;31m# Cross-validation loop\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mtrain_index\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtest_index\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtscv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m         \u001b[0mcv_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcv_test\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtrain_index\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtest_index\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m         \u001b[0;31m# Fit SARIMAX model\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'list' object has no attribute 'iloc'"
     ]
    }
   ],
   "source": [
    "# Define a range of hyperparameters to test\n",
    "param_dist = {\"order\": [(p, d, q) for p in range(3) for d in [0, 1, 2] for q in range(3)],\n",
    "    \"seasonal_order\": [(P, D, Q, 12) for P in range(3) for D in [0, 1, 2] for Q in range(3)]}\n",
    "\n",
    "# Initialize a random parameter sampler\n",
    "param_list = list(ParameterSampler(param_dist, n_iter=50))\n",
    "\n",
    "# Define Time Series cross-validator\n",
    "tscv = TimeSeriesSplit(n_splits=4)\n",
    "\n",
    "best_aic = np.inf\n",
    "best_bic = np.inf\n",
    "best_params = None\n",
    "\n",
    "# Cross-validation and hyperparameter tuning\n",
    "for params in param_list:\n",
    "    aic_scores = []\n",
    "    bic_scores = []\n",
    "\n",
    "    # Cross-validation loop\n",
    "    for train_index, test_index in tscv.split(df):\n",
    "        cv_train, cv_test = df.iloc[train_index], df.iloc[test_index]\n",
    "\n",
    "        # Fit SARIMAX model\n",
    "        sarima = SARIMAX(cv_train['PRECIO OPEP'], exog=cv_train['PRECIO OPEP'],\n",
    "                         order=params['order'], seasonal_order=params['seasonal_order'])\n",
    "        sarima_results = sarima.fit()\n",
    "\n",
    "        # Save AIC and BIC scores\n",
    "        aic_scores.append(sarima_results.aic)\n",
    "        bic_scores.append(sarima_results.bic)\n",
    "\n",
    "    # Average AIC and BIC scores\n",
    "    mean_aic = np.mean(aic_scores)\n",
    "    mean_bic = np.mean(bic_scores)\n",
    "\n",
    "    # Update best parameters if current model has a lower AIC and BIC\n",
    "    if mean_aic < best_aic and mean_bic < best_bic:\n",
    "        best_aic = mean_aic\n",
    "        best_bic = mean_bic\n",
    "        best_params = params\n",
    "\n",
    "# Print the best parameters and the corresponding AIC and BIC\n",
    "print('Best parameters:', best_params)\n",
    "print('Best AIC:', best_aic)\n",
    "print('Best BIC:', best_bic)\n",
    "\n",
    "# Fit the best model\n",
    "best_model = SARIMAX(df['PRECIO OPEP'], exog=df['PRECIO OPEP'],\n",
    "                     order=best_params['order'], seasonal_order=best_params['seasonal_order'])\n",
    "best_model_fit = best_model.fit()\n",
    "\n",
    "\n",
    "# Define future US Dollar Index\n",
    "future_WTI_price = [101.64, 103.06, 103.66, 104.33, 103.57, 102.59, 99.42, 99.48, 101.97, 102.85, 103.33, 102.4, \n",
    "                          101.23, 100.08, 99.78, 98.72, 97.62, 98.34]\n",
    "\n",
    "\n",
    "# Create forecast object\n",
    "forecast_object = best_model_fit.get_forecast(steps=18, exog=np.array(future_WTI_price).reshape(-1, 1),alpha=0.2)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Extract prediction mean\n",
    "mean = forecast_object.predicted_mean\n",
    "\n",
    "\n",
    "# Extract the forecast dates\n",
    "datescf = pd.date_range(start=df.index[-1], periods=18, freq='MS')\n",
    "\n",
    "\n",
    "# Predictions on historical data\n",
    "in_sample_forecast = best_model_fit.get_prediction(start=pd.to_datetime('2019-01-02'), \n",
    "                                                   end=df.index[-1], \n",
    "                                                   dynamic=False, \n",
    "                                                   exog=df['PRECIO OPEP'][df.index >= pd.to_datetime('2019-01-02')])\n",
    "\n",
    "\n",
    "in_sample_mean = in_sample_forecast.predicted_mean\n",
    "\n",
    "\n",
    "# Replace negative predicted values with 0\n",
    "in_sample_mean[in_sample_mean < 0] = 0\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Confidence intervals for the in-sample data\n",
    "in_sample_conf_int = in_sample_forecast.conf_int()\n",
    "\n",
    "\n",
    "# Correct any negative lower confidence levels in the in-sample data\n",
    "in_sample_conf_int[in_sample_conf_int.iloc[:, 0] < 0] = 0\n",
    "\n",
    "\n",
    "# Confidence intervals for the out-of-sample data\n",
    "conf_int = best_model_fit.get_forecast(steps=len(future_WTI_price), exog=future_WTI_price).conf_int()\n",
    "\n",
    "\n",
    "# Correct any negative lower confidence levels in the out-of-sample data\n",
    "conf_int[conf_int.iloc[:, 0] < 0] = 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a range of hyperparameters to test\n",
    "param_dist = {\"order\": [(p, d, q) for p in range(3) for d in [0, 1, 2] for q in range(3)],\n",
    "    \"seasonal_order\": [(P, D, Q, 12) for P in range(3) for D in [0, 1, 2] for Q in range(3)]}\n",
    "\n",
    "\n",
    "# Initialize a random parameter sampler\n",
    "param_list = list(ParameterSampler(param_dist, n_iter=50))\n",
    "\n",
    "\n",
    "# Define Time Series cross-validator\n",
    "tscv = TimeSeriesSplit(n_splits=5)\n",
    "\n",
    "\n",
    "best_aic = np.inf\n",
    "best_bic = np.inf\n",
    "best_params = None\n",
    "\n",
    "\n",
    "# Cross-validation and hyperparameter tuning\n",
    "for params in param_list:\n",
    "    aic_scores = []\n",
    "    bic_scores = []\n",
    "\n",
    "\n",
    "    # Cross-validation loop\n",
    "    for train_index, test_index in tscv.split(df):\n",
    "        cv_train, cv_test = df.iloc[train_index], df.iloc[test_index]\n",
    "\n",
    "\n",
    "        # Fit SARIMAX model\n",
    "        sarima = SARIMAX(cv_train['Crude_Oil_WTI_($/bbl)'], exog=cv_train['US Dollar Index'],\n",
    "                         order=params['order'], seasonal_order=params['seasonal_order'])\n",
    "        sarima_results = sarima.fit()\n",
    "\n",
    "\n",
    "        # Save AIC and BIC scores\n",
    "        aic_scores.append(sarima_results.aic)\n",
    "        bic_scores.append(sarima_results.bic)\n",
    "\n",
    "\n",
    "    # Average AIC and BIC scores\n",
    "    mean_aic = np.mean(aic_scores)\n",
    "    mean_bic = np.mean(bic_scores)\n",
    "\n",
    "\n",
    "    # Update best parameters if current model has a lower AIC and BIC\n",
    "    if mean_aic < best_aic and mean_bic < best_bic:\n",
    "        best_aic = mean_aic\n",
    "        best_bic = mean_bic\n",
    "        best_params = params\n",
    "\n",
    "\n",
    "# Print the best parameters and the corresponding AIC and BIC\n",
    "print('Best parameters:', best_params)\n",
    "print('Best AIC:', best_aic)\n",
    "print('Best BIC:', best_bic)\n",
    "\n",
    "\n",
    "# Fit the best model\n",
    "best_model = SARIMAX(df['Crude_Oil_WTI_($/bbl)'], exog=df['US Dollar Index'],\n",
    "                     order=best_params['order'], seasonal_order=best_params['seasonal_order'])\n",
    "best_model_fit = best_model.fit()\n",
    "\n",
    "\n",
    "# Define future US Dollar Index\n",
    "future_us_dollar_index = [101.64, 103.06, 103.66, 104.33, 103.57, 102.59, 99.42, 99.48, 101.97, 102.85, 103.33, 102.4, \n",
    "                          101.23, 100.08, 99.78, 98.72, 97.62, 98.34]\n",
    "\n",
    "\n",
    "# Create forecast object\n",
    "forecast_object = best_model_fit.get_forecast(steps=18, exog=np.array(future_us_dollar_index).reshape(-1, 1),alpha=0.2)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Extract prediction mean\n",
    "mean = forecast_object.predicted_mean\n",
    "\n",
    "\n",
    "# Extract the forecast dates\n",
    "datescf = pd.date_range(start=df.index[-1], periods=18, freq='MS')\n",
    "\n",
    "\n",
    "# Predictions on historical data\n",
    "in_sample_forecast = best_model_fit.get_prediction(start=pd.to_datetime('1983-05-01'), \n",
    "                                                   end=df.index[-1], \n",
    "                                                   dynamic=False, \n",
    "                                                   exog=df['US Dollar Index'][df.index >= pd.to_datetime('1983-04-01')])\n",
    "\n",
    "\n",
    "in_sample_mean = in_sample_forecast.predicted_mean\n",
    "\n",
    "\n",
    "# Replace negative predicted values with 0\n",
    "in_sample_mean[in_sample_mean < 0] = 0\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Confidence intervals for the in-sample data\n",
    "in_sample_conf_int = in_sample_forecast.conf_int()\n",
    "\n",
    "\n",
    "# Correct any negative lower confidence levels in the in-sample data\n",
    "in_sample_conf_int[in_sample_conf_int.iloc[:, 0] < 0] = 0\n",
    "\n",
    "\n",
    "# Confidence intervals for the out-of-sample data\n",
    "conf_int = best_model_fit.get_forecast(steps=len(future_us_dollar_index), exog=future_us_dollar_index).conf_int()\n",
    "\n",
    "\n",
    "# Correct any negative lower confidence levels in the out-of-sample data\n",
    "conf_int[conf_int.iloc[:, 0] < 0] = 0"
   ]
  }
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