Ch24_QuantileRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantile Regressions\n",
    "\n",
    "This notebook illustrates quantile regressions.\n",
    "\n",
    "As an alternative, consider the [QuantileRegressions.jl](https://github.com/pkofod/QuantileRegressions.jl) package."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions\n",
    "\n",
    "The key function used in this notebook `QuantRegrIRLS()` is from the (local) `FinEcmt_OLS` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "MyModulePath = joinpath(pwd(),\"src\")\n",
    "!in(MyModulePath,LOAD_PATH) && push!(LOAD_PATH,MyModulePath);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "using FinEcmt_OLS, DelimitedFiles, Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "using Plots\n",
    "default(size = (480,320),fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size: 15355\n"
     ]
    }
   ],
   "source": [
    "xx  = readdlm(\"Data/FFdFactors.csv\",',',skipstart=1)\n",
    "xx  = xx[:,2]            #equity market excess returns\n",
    "\n",
    "y = xx[2:end]            #dependent variable\n",
    "x = xx[1:end-1]          #regressor in an AR(1)\n",
    "\n",
    "T   = size(y,1)\n",
    "println(\"Sample size: $T\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Function for Quantile Regressions\n",
    "\n",
    "The `QuantRegrIRLS()` function from the `FinEcmt_OLS` estimates a quantile regression. It uses a simple iterative (re-)weighted least squares (IRLS) approach. It can be shown that a linear programming approach gives almost identical results for this data set. However, it seems that the iterative approach is quicker in really large data sets. The function returns several different calculations of the standard errors: see the code below and the lecture notes for details.\n",
    "\n",
    "The subsequent cells calculate and show the results. The calculations take some time.\n",
    "\n",
    "### A Remark on the Code\n",
    "- The arrays in the iteration are pre-allocated and then the new results overwrite the old ones, in an attempt to decrease the memory usage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "```\n",
       "QuantRegrIRLS(y,x,q=0.5;prec=1e-8,epsu=1e-6,maxiter=1000)\n",
       "```\n",
       "\n",
       "Estimate a quantile regression for quantile `q`. The outputs are the point estimates and three different variance-covariance matrices of the estimates.\n",
       "\n",
       "### Input\n",
       "\n",
       "  * `y::Vector`:     T vector, dependent variable\n",
       "  * `x::VecOrMat`:   TXK, regressors (including any constant)\n",
       "  * `q::Number`:     quantile to estimate at, 0<q<1\n",
       "  * `prec::Float64`: convergence criterion, 1e-8\n",
       "  * `epsu::Float64`: lower bound on 1/weight, 1e-6\n",
       "  * `maxiter::Int`:  maximum number of iterations, 1000\n",
       "\n",
       "### Output\n",
       "\n",
       "  * `theta::Vector`: K vector, estimated coefficients\n",
       "  * `vcv::Matrix`:   KxK, traditional covariance matrix\n",
       "  * `vcv2::Matrix`:  KxK, Powell (1991) covariance matrix\n",
       "  * `vcv3::Matrix`:  KxK, Powell (1991) covariance matrix, uniform\n",
       "\n",
       "### Remarks\n",
       "\n",
       "1. `while maximum(abs,b - b_old) > prec ...end` creates a loop that continues as long as  the new and previous estimates differ more than `prec`. However, once the number of  iterations exceed `maxiter` then the execution is stopped.\n",
       "2. `u .= max.(u,epsu)` limits how small `u` can become which makes the algorithm more stable (recall: the next command is `x./u`).\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@doc2 QuantRegrIRLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#using CodeTracking\n",
    "#println(@code_string QuantRegrIRLS([1],[1],0.05))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mquantile regression coefs:\u001b[22m\u001b[39m\n",
      "\n",
      "quantile         c     slope\n",
      "0.01        -2.568     0.139\n",
      "0.05        -1.433     0.158\n",
      "0.25        -0.410     0.146\n",
      "0.5          0.047     0.067\n",
      "0.75         0.477     0.024\n",
      "0.95         1.409    -0.028\n",
      "0.99         2.582    -0.188\n",
      "\n",
      "\n",
      "\u001b[31m\u001b[1mThe function QuantRegrIRLS also outputs different variance-covariance matrices. Compare them.\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "xGrid = quantile(x,0.01:0.01:0.99)                 #quantiles of the regressor, for plots\n",
    "xGrid = [ones(size(xGrid)) xGrid]\n",
    "\n",
    "qM = [0.01,0.05,0.25,0.5,0.75,0.95,0.99]           #quantiles\n",
    "\n",
    "cx = [ones(T) x]                                   #[constant regressors]\n",
    "\n",
    "bM    = fill(NaN,length(qM),2)                     #to store regression coeffs\n",
    "qPred = fill(NaN,length(qM),size(xGrid,1))         #to store predicted values\n",
    "for i = 1:length(qM)\n",
    "    #local b_q\n",
    "    b_q        = QuantRegrIRLS(y,cx,qM[i])[1]\n",
    "    bM[i,:]    = b_q\n",
    "    qPred[i,:] = xGrid*b_q\n",
    "end\n",
    "\n",
    "printblue(\"quantile regression coefs:\\n\")\n",
    "printmat(bM;colNames=[\"c\",\"slope\"],rowNames=string.(qM),cell00=\"quantile\")\n",
    "\n",
    "printred(\"\\nThe function QuantRegrIRLS also outputs different variance-covariance matrices. Compare them.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lab = permutedims([\"quantile $(qM[i])\" for i=1:length(qM)])\n",
    "\n",
    "p1 = plot( xGrid[:,2],qPred',\n",
    "           label = lab,\n",
    "           xlabel = \"lagged return\",\n",
    "           ylabel = \"fitted return\",\n",
    "           title = \"Fitted values for various quantiles\" )\n",
    "display(p1)"
   ]
  },
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