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Copy pathAAA_RUN_KANSM2_Est_LB.py
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AAA_RUN_KANSM2_Est_LB.py
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from globl import *
from functions import *
from AAB_KAGM_Estimation_NelderMead_file import AAB_KAGM_Estimation_NelderMead
from AAC_KAGM_SingleLoop_file import *
from AAH_EMS_N23_function_file import *
from AAL_CommonSaveName_file import *
from AAF_FiniteDifferenceHessian_file import *
import numpy
import datetime
import math
import scipy
import scipy.optimize
import csv
# Hyperparameters.
N = 2 # FIXED: Number of factors.
dTau = 0.01 # OPTION: Spacing for TauGrid, used to numerically obtain R.
KappaP_Constraint = 'Direct' # FIXED: KappaP matrix values are set directly, (but subject to an eigenvalue constraint in 'AAC_EKF_CAB_GATSM_SingleLoop').
ZLB_Imposed = 1 # FIXED: 0=ANSM(2) or 1=K-ANSM(2).
DailyIterations = 200 # OPTION: Sets number of iterations between interim saves.
IEKF_Count = -1e-5 # OPTION: EKF if 0, IEKF steps if >0, tolerance if <0 (e.g. -1e-5).
FinalNaturalParametersGiven = 1 # OPTION: Full estimation if 0 (the Optimization toolbox is required), partial estimation with given parameters if 0.
HessianRequired = 0 # OPTION: Omits Hessian and standard errors if 0, calculates them if 1.
# GSW US data file.
Country = 'UK'
DataFrequency = 'Monthly'
DataFileName=Country+'_GSW_Govt'
#load([DataFileName,'.mat'])
# DailyDateIndex DailyYieldCurveData Maturities MonthlyDateIndex MonthlyYieldCurveData WeeklyDateIndex WeeklyYieldCurveData
Maturities=numpy.array([0.25,0.5,1,2,3,4,5,7,10,15,20,30])
sub_datenum = datetime.date(1899,12,30).toordinal() + 366
daily_file_name = Country+'_Daily.csv'
daily_data = numpy.genfromtxt(daily_file_name, delimiter=',')
DailyDateIndex = daily_data[:, 0].copy().astype('int')
DailyDateIndex=DailyDateIndex.__add__(sub_datenum)
DailyYieldCurveData = daily_data[:, 1:].copy()
weekly_file_name = Country+'_Weekly.csv'
weekly_data = numpy.genfromtxt(weekly_file_name, delimiter=',')
WeeklyDateIndex = weekly_data[:, 0].copy().astype('int')
WeeklyDateIndex=WeeklyDateIndex.__add__(sub_datenum)
WeeklyYieldCurveData = weekly_data[:, 1:].copy()
month_file_name = Country+'_Monthly.csv'
month_data = numpy.genfromtxt(month_file_name, delimiter=',')
MonthlyDateIndex = month_data[:, 0].copy().astype('int')
MonthlyDateIndex= MonthlyDateIndex.__add__(sub_datenum)
MonthlyYieldCurveData = month_data[:, 1:].copy()
#print numpy.shape(DailyDateIndex)
#print numpy.shape(DailyYieldCurveData)
#print numpy.shape(Maturities)
#print numpy.shape(MonthlyDateIndex)
#print numpy.shape(MonthlyYieldCurveData)
#print numpy.shape(WeeklyDateIndex)
#print numpy.shape(WeeklyYieldCurveData)
FirstDay = DailyDateIndex[0]
LastDay = DailyDateIndex[-1]
#FirstDay = datetime_to_matlab_datenum(datetime.datetime.strptime('30-Dec-1994', "%d-%b-%Y")) # Start of 30-year data.
#LastDay = datetime_to_matlab_datenum(datetime.datetime.strptime('31-Jul-2013', "%d-%b-%Y"))
SampleMaturities = numpy.array([0.25, 0.5, 1, 2, 3, 5, 7, 10, 30])
# Set starting parameters.
# These lines set the estimated values from Krippner (2015).
#LoadName='BOOK_US_GSW_Govt_OIS_rL_30_K_AFNSM2_Monthly_IEKF_E-5_Final_2014_8_31_10_52_X';
#load([LoadName,'.mat'],'FinalNaturalParameters');
# FinalNaturalParameters
FinalNaturalParameters_country="FinalNaturalParameters_"+Country+".dat"
FinalNaturalParameters = numpy.loadtxt(FinalNaturalParameters_country)
InitialNaturalParameters = numpy.copy(FinalNaturalParameters)
# Select the required data from the yield curve data file.
IncludeMaturities = numpy.array([x in SampleMaturities for x in Maturities])
if (DataFrequency == 'Daily'):
(StartT,) = numpy.where(DailyDateIndex==FirstDay)
(EndT,) = numpy.where(DailyDateIndex==LastDay)
YieldCurveDateIndex = DailyDateIndex[StartT:EndT+1]
YieldCurveData = DailyYieldCurveData[StartT:EndT+1,IncludeMaturities]
Dt = (YieldCurveDateIndex[-1] - YieldCurveDateIndex[0] + 1) / (len(YieldCurveDateIndex) * 365.25)
Iterations = numpy.copy(DailyIterations)
elif (DataFrequency == 'Weekly'):
# Find earliest Friday consistent with FirstDay.
ReferenceFriday = datetime_to_matlab_datenum(datetime.datetime.strptime('24-May-2013', "%d-%b-%Y"))
WeeksToStepBackForStart = numpy.floor((ReferenceFriday - FirstDay) / 7)
FirstWeek = ReferenceFriday - 7 * WeeksToStepBackForStart
# Find latest Friday consistent with LastDay.
WeeksToStepBackForEnd = 1 + numpy.floor((ReferenceFriday - LastDay) / 7)
LastWeek = ReferenceFriday - 7 * WeeksToStepBackForEnd
(StartT,) = numpy.where(WeeklyDateIndex==FirstWeek)
(EndT,) = numpy.where(WeeklyDateIndex==LastWeek)
YieldCurveDateIndex = WeeklyDateIndex[StartT:EndT+1]
YieldCurveData = WeeklyYieldCurveData[StartT:EndT+1,IncludeMaturities]
Dt = 7 / 365.25
Iterations = DailyIterations * 5
else:
# Find earliest end-month consistent with FirstDay.
[FirstYear, FirstMonth] = [datetime.datetime.fromordinal(numpy.int(FirstDay-366)).year, datetime.datetime.fromordinal(numpy.int(FirstDay-366)).month]
if FirstMonth == 12:
FirstYear = FirstYear+1
FirstMonth = 0
FirstMonth = numpy.int(datetime_to_matlab_datenum(datetime.datetime(FirstYear, FirstMonth+1, 1)) - 1)
# Find latest end-month consistent with LastDay.
[LastYear, LastMonth] = [datetime.datetime.fromordinal(numpy.int(LastDay-366)).year, datetime.datetime.fromordinal(numpy.int(LastDay-366)).month]
if LastMonth == 12:
LastYear = LastYear+1
LastMonth = 0
LastMonth1 = numpy.int(datetime_to_matlab_datenum(datetime.datetime(LastYear, LastMonth+1, 1)) - 1)
if (LastMonth1 != LastDay):
if LastMonth == 0:
LastYear = LastYear-1
LastMonth = 12
LastMonth1 = datetime_to_matlab_datenum(datetime.datetime(LastYear, LastMonth, 1)) - 1
(StartT,) = numpy.where(MonthlyDateIndex==FirstMonth)
(EndT,) = numpy.where(MonthlyDateIndex==LastMonth1)
if ((numpy.size(StartT) > 0) and (numpy.size(EndT) > 0)):
YieldCurveDateIndex = MonthlyDateIndex[StartT:EndT+1]
YieldCurveData = MonthlyYieldCurveData[StartT:EndT+1,IncludeMaturities]
else:
YieldCurveDateIndex = numpy.array([])
YieldCurveData = numpy.array([])
Dt = 1.0 / 12
Iterations = DailyIterations * 21
Tau_K = numpy.copy(SampleMaturities)
# Estimation.
if (FinalNaturalParametersGiven == 1):
print 'Finalizing model K-AFNSM(2) for ' + Country + " using %i" % Maturities[0] + "-%i" % SampleMaturities[-1] + ' year data at ' + DataFrequency + ' frequency for period ' + matlab_datenum_to_datetime(YieldCurveDateIndex[0]).strftime('%d-%b-%Y') + ' to ' + matlab_datenum_to_datetime(YieldCurveDateIndex[-1]).strftime('%d-%b-%Y')
FinalNaturalParameters = numpy.copy(InitialNaturalParameters)
FINAL = 1
Exitflag = -1
[Fval, x_T] = AAC_KAGM_SingleLoop(numpy.matrix(YieldCurveData), Tau_K,N, FinalNaturalParameters, Dt, dTau, KappaP_Constraint, ZLB_Imposed, IEKF_Count, FINAL)
Time0 = 0
Time1 = 0
Output = 'Final parameters given'
rL = FinalNaturalParameters[0]
KappaQ2 = FinalNaturalParameters[1]
KappaP = numpy.array([[FinalNaturalParameters[2], FinalNaturalParameters[3]], [FinalNaturalParameters[4], FinalNaturalParameters[5]]])
ThetaP = numpy.array([[FinalNaturalParameters[6]], [FinalNaturalParameters[7]]])
Sigma1 = FinalNaturalParameters[8]
Sigma2 = FinalNaturalParameters[9]
Rho12 = FinalNaturalParameters[10]
else:
# Estimate final parameters.
print 'Estimating K-AFNSM(2) for ' + Country + " using %i" % SampleMaturities[0] + "-%i" % SampleMaturities[-1] + ' year data at ' + DataFrequency + ' frequency for period ' + matlab_datenum_to_datetime(YieldCurveDateIndex[0]).strftime('%d-%b-%Y') + ' to ' + matlab_datenum_to_datetime(YieldCurveDateIndex[-1]).strftime('%d-%b-%Y')
Exitflag = 0
while (Exitflag == 0):
if (KappaP_Constraint == 'Direct'):
InitialParameters = numpy.copy(InitialNaturalParameters)
tmp_func = lambda x: x/(1+numpy.abs(x))-InitialNaturalParameters[9]
InitialParameters[9] = scipy.optimize.fsolve(tmp_func,1)
elif (KappaP_Constraint == 'S/A'):
print 'Nothing here.'
# Extended Kalman filter estimation.
#Time0 = matlab_now(datetime.datetime.now())
Time0 = datetime_to_matlab_datenum(datetime.datetime.now())
FINAL = 0
Max_IEKF_Count = 0
Max_IEKF_Point = 0
[x_T, FinalParameters, Fval, Exitflag, Output] = AAB_KAGM_Estimation_NelderMead(YieldCurveData, Tau_K, N, InitialParameters, Dt, dTau, KappaP_Constraint, ZLB_Imposed, IEKF_Count, FINAL, Iterations)
Time1 = matlab_now(datetime.datetime.now())
if (KappaP_Constraint == 'Direct'):
# Take the absolute value of Sigma parameters.
FinalNaturalParameters = FinalParameters;
FinalNaturalParameters[8] = abs(FinalParameters[8])
FinalNaturalParameters[9] = abs(FinalParameters[9])
# Convert correlation parameters into correlations.
FinalNaturalParameters[10] = FinalParameters[10] / (1 + abs(FinalParameters[10]))
FinalNaturalParameters[11:] = abs(FinalParameters[11:])
# Calculate the state equation quantities based on parameter values.
KappaQ = numpy.array([[0, 0], [FinalNaturalParameters[0], 0]])
KappaP = numpy.array([[FinalNaturalParameters[1], FinalNaturalParameters[2]], [FinalNaturalParameters[3], FinalNaturalParameters[4]]])
D, V = numpy.linalg.eig(KappaP)
d1 = D[0,0]
d2 = D[1,1]
if ((d1.real < 0) or (d2.real < 0)):
if (d1.real < 0):
d1 = 1e-6 + d1.imag * 1j
if (d2.real < 0):
d2 = 1e-6 + d2.imag * 1j
D = numpy.diag([d1, d2])
tmp1 = numpy.matrix(V)
tmp2 = tmp1 * numpy.matrix(numpy.reshape(D, (len(D),1)))
KappaP = numpy.array(numpy.real(numpy.linalg.solve(tmp1.getH(), tmp2.getH()).getH()))
FinalNaturalParameters[2] = KappaP[0,0]
FinalNaturalParameters[3] = KappaP[0,1]
FinalNaturalParameters[4] = KappaP[1,0]
FinalNaturalParameters[5] = KappaP[1,1]
elif (KappaP_Constraint == 'S/A'):
print 'Nothing here'
rL = FinalNaturalParameters[0]
KappaQ2 = FinalNaturalParameters[1]
KappaP = numpy.array([[FinalNaturalParameters[2], FinalNaturalParameters[3]], [FinalNaturalParameters[4], FinalNaturalParameters[5]]])
ThetaP = numpy.array([[FinalNaturalParameters[6]], [FinalNaturalParameters[7]]])
Sigma1 = FinalNaturalParameters[8]
Sigma2 = FinalNaturalParameters[9]
Rho12 = FinalNaturalParameters[10]
# disp(Exitflag)
print [Max_IEKF_Point, Max_IEKF_Count]
print Fval
print FinalNaturalParameters[0:10]
#plotyy(1:length(x_T),x_T',1:length(x_T),sum(x_T)')
#pause 0.1
# Create figure
figure = pyplot.figure(num=None, figsize=(8, 6), dpi=100, facecolor='w')
subplot1 = figure.add_subplot(1,1,1, position=[0.15, 0.10, 0.75, 0.80], frame_on=True, zorder=0)
tmp1 = numpy.arange(0, max(numpy.shape(x_T))+1)
subplot1.plot(tmp1, x_T.getH(), linewidth=2, marker='', markersize=3, zorder=1, label="")
subplot2 = subplot1.twinx()
subplot1.plot(tmp1, numpy.sum(x_T).getH(), linewidth=2, marker='', markersize=3, zorder=1, label="")
SaveName = AAL_CommonSaveName(DataFileName, ZLB_Imposed, IEKF_Count, SampleMaturities, N, DataFrequency, FINAL, -10);
disp(SaveName)
figure1 = pyplot.figure(num=None, figsize=(8, 6), dpi=100, facecolor='w')
figure1.plot(tmp1, x_T.getH(), linewidth=2, marker='', markersize=3, zorder=1, label="")
# Save final output in CSV file.
NaturalParameterStandardErrors = -9.999 * numpy.ones(numpy.size(FinalNaturalParameters))
numpy.savetxt(SaveName+".csv", FinalNaturalParameters, fmt='%25.15e', delimiter=',', newline='\n')
# Reset InitialNaturalParameters for next iteration.
InitialNaturalParameters = numpy.copy(FinalNaturalParameters)
#
# Diagnostics and output.
# Calculate Hessian and standard errors for parameters, if required.
if (HessianRequired == 1):
# Calculate Hessian and standard errors for natural model parameters.
FINAL = 1
NaturalHessian = AAF_FiniteDifferenceHessian(AAC_KAGM_SingleLoop, FinalNaturalParameters, 1e-10, YieldCurveData, Tau_K, N, Dt, dTau, KappaP_Constraint, ZLB_Imposed, IEKF_Count, FINAL)
NaturalParameterStandardErrors = numpy.sqrt(numpy.abs(numpy.diag(numpy.linalg.inv(NaturalHessian))));
else:
NaturalParameterStandardErrors = -9.999 * numpy.ones(numpy.size(FinalNaturalParameters))
# Display output.
dTime = Time1 - Time0
print dTime*24, 'hours (=', dTime*24*60, 'minutes)'
print Output
print Exitflag
print Fval
print InitialNaturalParameters[0:10]
print FinalNaturalParameters[0:10]
print NaturalParameterStandardErrors[0:10]
KappaQ = numpy.matrix([[0,0], [0,KappaQ2]])
print KappaP, numpy.linalg.eig(KappaP), KappaQ-KappaP
(T,K) = numpy.shape(YieldCurveData)
Residuals = numpy.ones((T,K)) * float('nan')
PlotCurves = 0
for t in range(0, T):
YieldCurveData_t = YieldCurveData[t,:]
(Fitted_R_t,tmp1) = AAD_KAGM_R_and_dR_dx(x_T[:,t], rL, KappaQ2, Sigma1, Sigma2, Rho12, Tau_K, dTau, ZLB_Imposed)
Fitted_R_t = numpy.reshape(numpy.array(Fitted_R_t), (numpy.size(Fitted_R_t),))
if (PlotCurves == 1):
figure = pyplot.figure(num=None, figsize=(8, 6), dpi=100, facecolor='w')
subplot = figure.add_subplot(1,1,1, position=[0.15, 0.10, 0.75, 0.80], frame_on=True, zorder=0)
subplot.plot(Tau_K, 100*Fitted_R_t, linewidth=2, marker='', markersize=3, zorder=1, label="")
subplot.plot(Tau_K, YieldCurveData_t, linestyle='', linewidth=2, marker='o', markersize=3, zorder=1, label="")
#ylim([-2 10]);
#pause(0.3)
Residual_t = 0.01 * YieldCurveData_t - Fitted_R_t
print numpy.shape(Residuals)
print numpy.shape(Residual_t)
Residuals[t,:] = Residual_t
#
RMSE_Residuals = numpy.sqrt(numpy.sum(numpy.multiply(Residuals,Residuals)) / T)
print numpy.mean(Residuals)
print RMSE_Residuals
Phi = KappaQ2
(SSR,EMS_Q,ETZ_Q) = AAH_EMS_N23_function(Phi, x_T, dTau)
# Save final output in MatLab file.
SaveName = AAL_CommonSaveName(DataFileName, ZLB_Imposed, IEKF_Count, SampleMaturities, N, DataFrequency, FINAL, -10);
print SaveName
# Save final output in CSV file.
#numpy.savetxt(SaveName+".csv", FinalNaturalParameters, fmt='%25.15e', delimiter=',', newline='\n')
#save(SaveName)
# Save final output in Excel spreadsheet.
RangeName = 'A2:O%i' % (max(numpy.shape(YieldCurveDateIndex))+1)
#xlswrite([SaveName,'.xlsm'],[YieldCurveDateIndex-datenum('30-Dec-1899'),YieldCurveData,100*x_T',100*SSR,100*EMS_Q,ETZ_Q],'D. Monthly',RangeName)
SSR_pos = SSR.copy()
SSR_pos[SSR_pos <= 0] = numpy.nan
fig,ax=pyplot.subplots()
pyplot.plot(SSR_pos*100,linewidth=2, marker='', markersize=3, zorder=1, label="slope", color='b')
SSR_neg = SSR.copy()
SSR_neg[SSR_neg > 0] = numpy.nan
pyplot.plot(SSR_neg*100,linewidth=2, marker='', markersize=3, zorder=1, label="slope", color='r')
a=ax.get_xticks()
y=[matlab_datenum_to_datetime(YieldCurveDateIndex[int(x)]).date().year for x in a[:-1]]
pyplot.xticks(a,y, rotation=90)
pyplot.ylabel('Percentage')
fig.suptitle('SSR', fontsize=20)
fig.savefig('SSR_'+DataFrequency+'.jpg')
fig,ax=pyplot.subplots()
pyplot.plot(EMS_Q*100,linewidth=2, marker='', markersize=3, zorder=1, label="slope")
a=ax.get_xticks()
y=[matlab_datenum_to_datetime(YieldCurveDateIndex[int(x)]).date().year for x in a[:-1]]
pyplot.xticks(a,y, rotation=90)
pyplot.ylabel('Percentage')
fig.suptitle('EMS', fontsize=20)
fig.savefig('EMS_'+DataFrequency+'.jpg')
fig,ax=pyplot.subplots()
pyplot.plot(ETZ_Q,linewidth=2, marker='', markersize=3, zorder=1, label="slope")
a=ax.get_xticks()
y=[matlab_datenum_to_datetime(YieldCurveDateIndex[int(x)]).date().year for x in a[:-1]]
pyplot.xticks(a,y, rotation=90)
pyplot.ylabel('Years')
fig.suptitle('ETZ', fontsize=20)
fig.savefig('ETZ_'+DataFrequency+'.jpg')
pyplot.show()
output=numpy.concatenate((YieldCurveData, 100*x_T.T), axis=1)
output=numpy.concatenate((output, 100*SSR.reshape((SSR.shape[0],1))), axis=1)
output=numpy.concatenate((output, 100*EMS_Q.reshape((SSR.shape[0],1))), axis=1)
output=numpy.concatenate((output, 100*ETZ_Q.reshape((SSR.shape[0],1))), axis=1)
date_str = [matlab_datenum_to_datetime(x).date().__str__() for x in YieldCurveDateIndex]
k=numpy.array(date_str)
k=k.reshape((len(k), 1))
with open(SaveName+'_final.csv', 'wb') as csvfile:
spamwriter = csv.writer(csvfile, delimiter=',')
header =['Date']+[str(x) for x in SampleMaturities]+['Level','Slope','SSR','EMS-Q','ETZ-Q']
spamwriter.writerow(header)
for i in range(len(date_str)):
data_to_write = list(k[i]) + list(output[i])
spamwriter.writerow(data_to_write)
print 'Finished'