library(tseries)
## Warning: package 'tseries' was built under R version 3.2.4
library(vars)
## Warning: package 'vars' was built under R version 3.2.4
## Loading required package: MASS
## Warning: package 'MASS' was built under R version 3.2.3
## Loading required package: strucchange
## Warning: package 'strucchange' was built under R version 3.2.3
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: sandwich
## Warning: package 'sandwich' was built under R version 3.2.3
## Loading required package: urca
## Warning: package 'urca' was built under R version 3.2.3
## Loading required package: lmtest
## Warning: package 'lmtest' was built under R version 3.2.3
library(MTS)
## Warning: package 'MTS' was built under R version 3.2.4
##
## Attaching package: 'MTS'
## The following object is masked from 'package:vars':
##
## VAR
library(stats)
library(forecast)
## Warning: package 'forecast' was built under R version 3.2.3
## Loading required package: timeDate
## Warning: package 'timeDate' was built under R version 3.2.3
## This is forecast 6.2
library(fGarch)
## Warning: package 'fGarch' was built under R version 3.2.4
## Loading required package: timeSeries
## Warning: package 'timeSeries' was built under R version 3.2.4
##
## Attaching package: 'timeSeries'
## The following object is masked from 'package:zoo':
##
## time<-
## Loading required package: fBasics
## Warning: package 'fBasics' was built under R version 3.2.4
##
## Rmetrics Package fBasics
## Analysing Markets and calculating Basic Statistics
## Copyright (C) 2005-2014 Rmetrics Association Zurich
## Educational Software for Financial Engineering and Computational Science
## Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
## https://www.rmetrics.org --- Mail to: info@rmetrics.org
library(Metrics)
## Warning: package 'Metrics' was built under R version 3.2.3
VolatilityPfizer <- read.csv("~/catedraeconometria/VolatilityPfizer.csv")
View(VolatilityPfizer)
attach(VolatilityPfizer)
plot(LN.Returns, type = "l")#Total Volatility of the sample
LN.Returns2<-c(LN.Returns[2:632])
LN.Returns3<-c(LN.Returns[632:1263])
plot(LN.Returns2, type ="l")
sd(LN.Returns2)
## [1] 0.01177139
abline(h=sd(LN.Returns2), col= "red")
ARCH1 <-garch(LN.Returns2, order = c(0,1))
##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 1.316374e-04 1.000e+00
## 2 5.000000e-02 1.000e+00
##
## IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
## 0 1 -2.490e+03
## 1 8 -2.490e+03 3.83e-05 7.17e-05 3.2e-05 1.7e+10 3.2e-06 6.26e+05
## 2 9 -2.490e+03 1.76e-07 1.82e-07 3.2e-05 2.0e+00 3.2e-06 6.89e-01
## 3 17 -2.491e+03 4.79e-04 8.41e-04 2.6e-01 2.0e+00 3.6e-02 6.88e-01
## 4 18 -2.491e+03 4.45e-05 3.25e-05 6.0e-02 0.0e+00 1.1e-02 3.25e-05
## 5 19 -2.491e+03 9.38e-06 8.23e-06 3.6e-02 0.0e+00 7.2e-03 8.23e-06
## 6 20 -2.491e+03 2.60e-07 2.43e-07 6.4e-03 0.0e+00 1.3e-03 2.43e-07
## 7 21 -2.491e+03 1.46e-09 1.44e-09 5.1e-04 0.0e+00 1.1e-04 1.44e-09
## 8 22 -2.491e+03 2.49e-13 2.50e-13 6.3e-06 0.0e+00 1.3e-06 2.50e-13
##
## ***** RELATIVE FUNCTION CONVERGENCE *****
##
## FUNCTION -2.491086e+03 RELDX 6.258e-06
## FUNC. EVALS 22 GRAD. EVALS 9
## PRELDF 2.498e-13 NPRELDF 2.498e-13
##
## I FINAL X(I) D(I) G(I)
##
## 1 1.228968e-04 1.000e+00 6.165e-02
## 2 1.055117e-01 1.000e+00 2.662e-06
summary(ARCH1)
##
## Call:
## garch(x = LN.Returns2, order = c(0, 1))
##
## Model:
## GARCH(0,1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.28446 -0.47859 0.03236 0.59481 3.07600
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## a0 1.229e-04 5.822e-06 21.109 < 2e-16 ***
## a1 1.055e-01 3.136e-02 3.364 0.000768 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Diagnostic Tests:
## Jarque Bera Test
##
## data: Residuals
## X-squared = 141.78, df = 2, p-value < 2.2e-16
##
##
## Box-Ljung test
##
## data: Squared.Residuals
## X-squared = 0.0076406, df = 1, p-value = 0.9303
OutofSampleEstimate <-garch(LN.Returns3,model=ARCH1)
##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 1.214574e-04 1.000e+00
## 2 5.000000e-02 1.000e+00
## 3 5.000000e-02 1.000e+00
##
## IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
## 0 1 -2.504e+03
## 1 7 -2.504e+03 8.33e-06 3.95e-04 1.0e-04 9.9e+09 1.0e-05 1.95e+06
## 2 8 -2.504e+03 9.78e-05 1.09e-04 5.0e-05 2.0e+00 5.0e-06 3.09e+00
## 3 9 -2.504e+03 4.77e-07 4.55e-07 5.0e-05 2.0e+00 5.0e-06 3.10e+00
## 4 17 -2.511e+03 2.78e-03 4.07e-03 4.5e-01 2.0e+00 8.2e-02 3.10e+00
## 5 20 -2.520e+03 3.69e-03 3.51e-03 7.4e-01 1.8e+00 3.3e-01 1.47e-01
## 6 22 -2.523e+03 1.11e-03 1.04e-03 7.9e-02 2.0e+00 6.6e-02 2.61e-01
## 7 24 -2.526e+03 1.14e-03 3.12e-03 2.3e-01 2.0e+00 2.6e-01 3.59e-01
## 8 33 -2.527e+03 2.65e-04 1.09e-03 2.5e-06 3.8e+00 3.6e-06 2.04e-03
## 9 34 -2.527e+03 1.15e-04 9.37e-05 2.4e-06 2.0e+00 3.6e-06 8.33e-04
## 10 35 -2.527e+03 4.02e-06 4.19e-06 2.4e-06 2.0e+00 3.6e-06 5.05e-04
## 11 36 -2.527e+03 5.25e-08 8.09e-08 2.5e-06 2.0e+00 3.6e-06 5.20e-04
## 12 44 -2.527e+03 1.86e-04 2.81e-04 2.5e-02 8.5e-01 3.5e-02 5.20e-04
## 13 45 -2.528e+03 1.89e-04 1.09e-04 1.7e-02 0.0e+00 3.2e-02 1.09e-04
## 14 46 -2.528e+03 2.01e-04 2.81e-04 6.6e-02 1.4e-01 1.2e-01 2.85e-04
## 15 47 -2.529e+03 8.67e-05 1.30e-04 8.8e-03 0.0e+00 1.4e-02 1.30e-04
## 16 48 -2.529e+03 1.51e-05 1.50e-05 7.0e-03 0.0e+00 1.3e-02 1.50e-05
## 17 49 -2.529e+03 9.06e-07 3.15e-06 1.9e-03 0.0e+00 3.4e-03 3.15e-06
## 18 50 -2.529e+03 9.15e-07 5.89e-07 1.7e-03 0.0e+00 2.7e-03 5.89e-07
## 19 52 -2.529e+03 1.24e-08 2.40e-08 1.5e-04 1.4e+00 2.8e-04 3.08e-08
## 20 55 -2.529e+03 3.72e-10 7.79e-11 1.8e-06 2.0e+00 3.2e-06 3.23e-09
## 21 58 -2.529e+03 1.20e-12 5.95e-13 1.9e-08 2.0e+00 3.4e-08 3.23e-09
## 22 60 -2.529e+03 1.14e-12 1.53e-13 4.8e-09 2.0e+00 8.9e-09 3.21e-09
## 23 67 -2.529e+03 -2.82e-14 5.95e-18 1.1e-14 6.6e+01 1.8e-14 3.23e-09
##
## ***** FALSE CONVERGENCE *****
##
## FUNCTION -2.528565e+03 RELDX 1.101e-14
## FUNC. EVALS 67 GRAD. EVALS 23
## PRELDF 5.947e-18 NPRELDF 3.227e-09
##
## I FINAL X(I) D(I) G(I)
##
## 1 9.382703e-06 1.000e+00 -8.538e-01
## 2 1.303874e-01 1.000e+00 -8.065e-03
## 3 8.040497e-01 1.000e+00 4.526e-02
ht.arch01=ARCH1$fit[,1]^2
lines(ht.arch01, col="red")
plot(ht.arch01, type ="l", col="red")
ht.arch01OUT= OutofSampleEstimate$fit[,1]^2
plot(ht.arch01OUT, type = "l")
#GARCH
GARCH11<-garchFit(formula = ~garch(1,1), data=window(LN.Returns2))
##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(0, 0)
## GARCH Model: garch
## Formula Variance: ~ garch(1, 1)
## ARMA Order: 0 0
## Max ARMA Order: 0
## GARCH Order: 1 1
## Max GARCH Order: 1
## Maximum Order: 1
## Conditional Dist: norm
## h.start: 2
## llh.start: 1
## Length of Series: 631
## Recursion Init: mci
## Series Scale: 0.01177139
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -0.47489747 0.4748975 0.04748975 TRUE
## omega 0.00000100 100.0000000 0.10000000 TRUE
## alpha1 0.00000001 1.0000000 0.10000000 TRUE
## gamma1 -0.99999999 1.0000000 0.10000000 FALSE
## beta1 0.00000001 1.0000000 0.80000000 TRUE
## delta 0.00000000 2.0000000 2.00000000 FALSE
## skew 0.10000000 10.0000000 1.00000000 FALSE
## shape 1.00000000 10.0000000 4.00000000 FALSE
## Index List of Parameters to be Optimized:
## mu omega alpha1 beta1
## 1 2 3 5
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 850.30503: 0.0474897 0.100000 0.100000 0.800000
## 1: 850.02841: 0.0474912 0.0876166 0.0978678 0.796098
## 2: 848.91841: 0.0474941 0.0849835 0.106479 0.805692
## 3: 847.92784: 0.0475034 0.0628228 0.109231 0.819612
## 4: 846.61737: 0.0475171 0.0567852 0.101684 0.844086
## 5: 844.47437: 0.0475517 0.0328066 0.0709751 0.888865
## 6: 844.25417: 0.0475521 0.0340894 0.0723589 0.890560
## 7: 844.16128: 0.0475545 0.0317976 0.0723550 0.891646
## 8: 844.01650: 0.0475623 0.0297069 0.0727926 0.896245
## 9: 843.89092: 0.0475762 0.0264970 0.0707200 0.899570
## 10: 843.78866: 0.0475998 0.0254649 0.0686796 0.904072
## 11: 843.72970: 0.0476485 0.0234816 0.0658921 0.907675
## 12: 843.69976: 0.0478148 0.0216264 0.0665558 0.910772
## 13: 843.67063: 0.0480115 0.0216399 0.0640117 0.912223
## 14: 843.66644: 0.0482485 0.0213342 0.0638922 0.913079
## 15: 843.66257: 0.0484872 0.0206984 0.0641191 0.913177
## 16: 843.64446: 0.0503190 0.0211587 0.0628132 0.913573
## 17: 843.63049: 0.0521515 0.0210274 0.0629332 0.914391
## 18: 843.61218: 0.0539843 0.0205310 0.0627424 0.914595
## 19: 843.59465: 0.0588129 0.0203514 0.0630731 0.914774
## 20: 843.59351: 0.0594662 0.0199967 0.0624720 0.915677
## 21: 843.59252: 0.0607768 0.0202466 0.0626675 0.915090
## 22: 843.59249: 0.0606142 0.0202089 0.0626408 0.915180
## 23: 843.59249: 0.0606133 0.0202082 0.0626401 0.915181
##
## Final Estimate of the Negative LLH:
## LLH: -1959.362 norm LLH: -3.10517
## mu omega alpha1 beta1
## 7.135028e-04 2.800164e-06 6.264006e-02 9.151812e-01
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu omega alpha1 beta1
## mu -6.242649e+06 -1.426562e+08 1.376111e+03 -8.621969e+03
## omega -1.426562e+08 -4.466928e+12 -3.424900e+08 -4.419837e+08
## alpha1 1.376111e+03 -3.424900e+08 -3.831231e+04 -4.116667e+04
## beta1 -8.621969e+03 -4.419837e+08 -4.116667e+04 -5.020593e+04
## attr(,"time")
## Time difference of 0.124012 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.2240131 secs
summary(GARCH11)
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 1), data = window(LN.Returns2))
##
## Mean and Variance Equation:
## data ~ garch(1, 1)
## <environment: 0x000000000bf699a8>
## [data = window(LN.Returns2)]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1
## 7.1350e-04 2.8002e-06 6.2640e-02 9.1518e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.135e-04 4.008e-04 1.780 0.0751 .
## omega 2.800e-06 1.430e-06 1.958 0.0503 .
## alpha1 6.264e-02 1.609e-02 3.893 9.9e-05 ***
## beta1 9.152e-01 2.194e-02 41.711 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 1959.362 normalized: 3.10517
##
## Description:
## Mon Apr 11 07:12:30 2016 by user: marcogeovanni
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 57.41037 3.416156e-13
## Shapiro-Wilk Test R W 0.9861067 1.043011e-05
## Ljung-Box Test R Q(10) 12.73282 0.2389964
## Ljung-Box Test R Q(15) 14.25003 0.5066571
## Ljung-Box Test R Q(20) 15.69082 0.7356102
## Ljung-Box Test R^2 Q(10) 6.675493 0.755684
## Ljung-Box Test R^2 Q(15) 9.639507 0.8417825
## Ljung-Box Test R^2 Q(20) 25.29698 0.1903048
## LM Arch Test R TR^2 7.463703 0.8255125
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -6.197661 -6.169469 -6.197741 -6.186711
predict(GARCH11)
## meanForecast meanError standardDeviation
## 1 0.0007135028 0.008433654 0.008433654
## 2 0.0007135028 0.008505832 0.008505832
## 3 0.0007135028 0.008575823 0.008575823
## 4 0.0007135028 0.008643713 0.008643713
## 5 0.0007135028 0.008709586 0.008709586
## 6 0.0007135028 0.008773519 0.008773519
## 7 0.0007135028 0.008835588 0.008835588
## 8 0.0007135028 0.008895860 0.008895860
## 9 0.0007135028 0.008954404 0.008954404
## 10 0.0007135028 0.009011282 0.009011282