Eleccion del mejor modelo GARCH
sebastian sosa perez
23/7/2020
library(readxl)
library(tseries)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(fGarch)## Loading required package: timeDate## Loading required package: timeSeries## Loading required package: fBasicsdata <- read_excel("C:/Users/daffy/Downloads/Mensuales-20200721-133058.xlsx", skip = 1)## New names:
## * `` -> ...1data=data[-length(data$...1),]
serie<-ts(data$`Tipo de cambio - promedio del periodo (S/ por US$) - Interbancario - Promedio`)plot(serie)
adf.test(serie)##
## Augmented Dickey-Fuller Test
##
## data: serie
## Dickey-Fuller = -1.0597, Lag order = 6, p-value = 0.9275
## alternative hypothesis: stationarydiff<-diff(as.numeric(serie))
plot(diff,type="l")
diff<-diff[-1]
adf.test(diff)## Warning in adf.test(diff): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: diff
## Dickey-Fuller = -6.1976, Lag order = 6, p-value = 0.01
## alternative hypothesis: stationaryacf(diff)
pacf(diff)
p<-c(2,0)
q<-c(1,2,0)
datos<-NULL
indice<- NULL
ata1=NULL
for(i in p){
for(a in q){
ata<- summary(arma(diff,order = c(i,a)))$aic
datos<- c(datos,ata)
atita<- paste(i,a)
indice<- c(indice,atita)
table<- data.frame("ARMA"=indice,"AIC"=datos)
ata1=table
}
}## Warning in optim(coef, err, gr = NULL, hessian = TRUE, ...): one-dimensional optimization by Nelder-Mead is unreliable:
## use "Brent" or optimize() directlyprint(ata1)## ARMA AIC
## 1 2 1 -991.4587
## 2 2 2 -991.3833
## 3 2 0 -990.0916
## 4 0 1 -995.1124
## 5 0 2 -993.4306
## 6 0 0 -971.4642El mejor modelo es un ARMA(0,1)
modelo<- arma(diff,order = c(0,1))
summary(modelo)##
## Call:
## arma(x = diff, order = c(0, 1))
##
## Model:
## ARMA(0,1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.121422 -0.017203 -0.001684 0.019549 0.098182
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## ma1 0.3553318 0.0641204 5.542 3e-08 ***
## intercept 0.0003626 0.0029026 0.125 0.901
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Fit:
## sigma^2 estimated as 0.001182, Conditional Sum-of-Squares = 0.3, AIC = -995.11residuos2<- na.omit(modelo$residuals)^2acf(residuos2)
pacf(residuos2)
modelo1<- garchFit(~garch(1,5),data = residuos2,trace = T)##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(0, 0)
## GARCH Model: garch
## Formula Variance: ~ garch(1, 5)
## ARMA Order: 0 0
## Max ARMA Order: 0
## GARCH Order: 1 5
## Max GARCH Order: 5
## Maximum Order: 5
## Conditional Dist: norm
## h.start: 6
## llh.start: 1
## Length of Series: 255
## Recursion Init: mci
## Series Scale: 0.002164843
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -5.43796108 5.437961 0.5437961 TRUE
## omega 0.00000100 100.000000 0.1000000 TRUE
## alpha1 0.00000001 1.000000 0.1000000 TRUE
## gamma1 -0.99999999 1.000000 0.1000000 FALSE
## beta1 0.00000001 1.000000 0.1600000 TRUE
## beta2 0.00000001 1.000000 0.1600000 TRUE
## beta3 0.00000001 1.000000 0.1600000 TRUE
## beta4 0.00000001 1.000000 0.1600000 TRUE
## beta5 0.00000001 1.000000 0.1600000 TRUE
## delta 0.00000000 2.000000 2.0000000 FALSE
## skew 0.10000000 10.000000 1.0000000 FALSE
## shape 1.00000000 10.000000 4.0000000 FALSE
## Index List of Parameters to be Optimized:
## mu omega alpha1 beta1 beta2 beta3 beta4 beta5
## 1 2 3 5 6 7 8 9
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 356.71787: 0.543796 0.100000 0.100000 0.160000 0.160000 0.160000 0.160000 0.160000
## 1: 355.97603: 0.543321 0.106605 0.103147 0.163110 0.162986 0.163417 0.162955 0.162591
## 2: 355.60609: 0.541799 0.111575 0.103433 0.159831 0.159355 0.160997 0.159214 0.157734
## 3: 346.25262: 0.476384 0.352949 0.186205 0.108351 0.0907383 0.145263 0.0859561 0.0339995
## 4: 341.23465: 0.391356 0.405459 0.390842 0.00660516 1.00000e-08 0.128689 1.00000e-08 1.00000e-08
## 5: 337.38201: 0.254881 0.460349 0.496737 1.00000e-08 1.00000e-08 0.0356458 0.144090 1.00000e-08
## 6: 335.38007: 0.292406 0.453374 0.510686 1.00000e-08 1.00000e-08 0.101270 0.0978221 1.00000e-08
## 7: 334.58721: 0.295088 0.428713 0.521204 1.00000e-08 1.00000e-08 0.0994741 0.0679574 1.00000e-08
## 8: 333.96895: 0.296974 0.423509 0.546686 1.00000e-08 1.00000e-08 0.129784 0.0623857 1.00000e-08
## 9: 333.69234: 0.298436 0.409535 0.557527 1.00000e-08 1.00000e-08 0.133284 0.0478348 1.00000e-08
## 10: 333.48381: 0.299387 0.406152 0.573767 1.00000e-08 1.00000e-08 0.149002 0.0521591 1.00000e-08
## 11: 333.32713: 0.312834 0.397654 0.608057 1.00000e-08 1.00000e-08 0.132682 0.0450714 1.00000e-08
## 12: 333.31331: 0.310723 0.398762 0.603130 1.00000e-08 1.00000e-08 0.136054 0.0463267 0.000389833
## 13: 333.24924: 0.309896 0.398667 0.607493 1.00000e-08 1.00000e-08 0.141674 0.0470864 8.57348e-07
## 14: 333.06167: 0.304026 0.384319 0.639902 1.00000e-08 1.00000e-08 0.171178 0.0341186 1.00000e-08
## 15: 333.04731: 0.303594 0.375388 0.649324 1.00000e-08 1.00000e-08 0.158943 0.0486405 1.00000e-08
## 16: 332.99664: 0.307792 0.377381 0.666817 1.00000e-08 1.00000e-08 0.154458 0.0368066 1.00000e-08
## 17: 332.99110: 0.308961 0.379655 0.673556 1.00000e-08 1.00000e-08 0.155348 0.0399580 0.00481331
## 18: 332.96242: 0.305592 0.382293 0.670578 1.00000e-08 1.00000e-08 0.154527 0.0400570 1.00000e-08
## 19: 332.95117: 0.306855 0.382306 0.678996 1.00000e-08 1.00000e-08 0.152574 0.0381422 0.00231546
## 20: 332.93741: 0.306387 0.382156 0.692553 1.00000e-08 1.00000e-08 0.149023 0.0361194 1.00000e-08
## 21: 332.91374: 0.296920 0.385409 0.686438 1.00000e-08 1.00000e-08 0.150363 0.0353241 0.00169715
## 22: 332.90859: 0.296456 0.385413 0.689450 1.00000e-08 1.00000e-08 0.148874 0.0386495 0.00199010
## 23: 332.90122: 0.295082 0.385905 0.692182 1.00000e-08 1.00000e-08 0.146744 0.0373606 0.000296801
## 24: 332.89273: 0.296245 0.386838 0.695828 1.00000e-08 1.00000e-08 0.145884 0.0366460 0.00207713
## 25: 332.88604: 0.295687 0.387475 0.699938 1.00000e-08 1.00000e-08 0.144064 0.0362705 0.000914115
## 26: 332.87476: 0.291804 0.389795 0.705008 1.00000e-08 1.00000e-08 0.141327 0.0378745 0.00162117
## 27: 332.86060: 0.292974 0.391186 0.713189 1.00000e-08 1.00000e-08 0.137890 0.0352522 0.00229156
## 28: 332.84935: 0.290778 0.390832 0.721134 1.00000e-08 1.00000e-08 0.135179 0.0373447 0.00112532
## 29: 332.84008: 0.290767 0.392779 0.730119 1.00000e-08 1.00000e-08 0.133315 0.0368326 0.00321619
## 30: 332.82522: 0.287762 0.393583 0.736194 1.00000e-08 1.00000e-08 0.128882 0.0346281 0.00299168
## 31: 332.81788: 0.287192 0.394982 0.745537 1.00000e-08 1.00000e-08 0.129116 0.0354383 0.00173625
## 32: 332.80791: 0.284452 0.394163 0.752299 1.00000e-08 1.00000e-08 0.124972 0.0361171 0.00352425
## 33: 332.79770: 0.283315 0.395617 0.760949 1.00000e-08 1.00000e-08 0.122656 0.0336746 0.00357982
## 34: 332.79487: 0.281287 0.395630 0.769019 1.00000e-08 1.00000e-08 0.119599 0.0347298 0.00180845
## 35: 332.76136: 0.268464 0.405448 0.829814 1.00000e-08 1.00000e-08 0.101401 0.0314693 0.00422851
## 36: 332.76015: 0.264287 0.399468 0.857180 1.00000e-08 1.00000e-08 0.0963046 0.0306363 0.00604896
## 37: 332.75669: 0.263310 0.406380 0.862556 1.00000e-08 1.00000e-08 0.0887676 0.0314555 0.00549533
## 38: 332.75667: 0.261935 0.406247 0.862256 1.00000e-08 1.00000e-08 0.0935537 0.0309101 0.00477625
## 39: 332.75532: 0.261994 0.405824 0.864348 1.00000e-08 1.00000e-08 0.0918800 0.0308666 0.00520809
## 40: 332.75512: 0.261782 0.405855 0.867078 1.00000e-08 1.00000e-08 0.0903847 0.0309289 0.00535105
## 41: 332.75512: 0.261607 0.405938 0.867901 1.00000e-08 1.00000e-08 0.0901403 0.0308938 0.00536878
## 42: 332.75512: 0.261472 0.406013 0.868539 1.00000e-08 1.00000e-08 0.0899519 0.0308822 0.00537842
## 43: 332.75512: 0.261472 0.406015 0.868543 1.00000e-08 1.00000e-08 0.0899511 0.0308802 0.00537798
##
## Final Estimate of the Negative LLH:
## LLH: -1231.774 norm LLH: -4.830485
## mu omega alpha1 beta1 beta2 beta3
## 5.660456e-04 1.902807e-06 8.685428e-01 1.000000e-08 1.000000e-08 8.995110e-02
## beta4 beta5
## 3.088018e-02 5.377977e-03
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu omega alpha1 beta1 beta2
## mu -75100864.15 4.586876e+09 -1.220671e+04 1.862682e+04 1.948589e+04
## omega 4586876040.77 -2.181944e+13 -7.067313e+06 -6.421670e+07 -3.762490e+07
## alpha1 -12206.71 -7.067313e+06 -3.322641e+01 -1.003544e+02 -1.196316e+02
## beta1 18626.82 -6.421670e+07 -1.003544e+02 5.451743e+02 -2.615641e+02
## beta2 19485.89 -3.762490e+07 -1.196316e+02 -2.615641e+02 1.786614e+03
## beta3 64074.07 -6.601167e+07 -8.540182e+01 -5.046462e+02 -2.008471e+02
## beta4 45465.40 -6.770394e+07 -1.088177e+02 -5.302876e+02 -2.620294e+02
## beta5 -24847.89 -1.014525e+08 -5.203549e+01 -5.191999e+02 -1.019285e+03
## beta3 beta4 beta5
## mu 6.407407e+04 4.546540e+04 -2.484789e+04
## omega -6.601167e+07 -6.770394e+07 -1.014525e+08
## alpha1 -8.540182e+01 -1.088177e+02 -5.203549e+01
## beta1 -5.046462e+02 -5.302876e+02 -5.191999e+02
## beta2 -2.008471e+02 -2.620294e+02 -1.019285e+03
## beta3 -4.699877e+02 -4.154809e+02 -4.709222e+02
## beta4 -4.154809e+02 -1.944734e+03 -7.828817e+02
## beta5 -4.709222e+02 -7.828817e+02 -3.991730e+03
## attr(,"time")
## Time difference of 0.03501487 secs
##
## --- END OF TRACE ---## Warning in sqrt(diag(fit$cvar)): Se han producido NaNs##
## Time to Estimate Parameters:
## Time difference of 0.133019 secssummary(modelo1)##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 5), data = residuos2, trace = T)
##
## Mean and Variance Equation:
## data ~ garch(1, 5)
## <environment: 0x00000000194253f8>
## [data = residuos2]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1 beta2 beta3
## 5.6605e-04 1.9028e-06 8.6854e-01 1.0000e-08 1.0000e-08 8.9951e-02
## beta4 beta5
## 3.0880e-02 5.3780e-03
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 5.660e-04 1.815e-04 3.118 0.00182 **
## omega 1.903e-06 3.323e-07 5.725 1.03e-08 ***
## alpha1 8.685e-01 3.395e-01 2.558 0.01051 *
## beta1 1.000e-08 NA NA NA
## beta2 1.000e-08 NA NA NA
## beta3 8.995e-02 1.155e-01 0.779 0.43610
## beta4 3.088e-02 2.678e-02 1.153 0.24891
## beta5 5.378e-03 1.686e-02 0.319 0.74975
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 1231.774 normalized: 4.830485
##
## Description:
## Thu Jul 23 16:50:14 2020 by user: daffy
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 4419.968 0
## Shapiro-Wilk Test R W 0.589105 0
## Ljung-Box Test R Q(10) 19.62779 0.03297636
## Ljung-Box Test R Q(15) 20.91263 0.1396441
## Ljung-Box Test R Q(20) 21.15406 0.388115
## Ljung-Box Test R^2 Q(10) 1.616987 0.9985224
## Ljung-Box Test R^2 Q(15) 3.033181 0.9995694
## Ljung-Box Test R^2 Q(20) 3.780562 0.9999708
## LM Arch Test R TR^2 2.675193 0.997435
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -9.598225 -9.487127 -9.600115 -9.553537modelo2<- garchFit(~garch(2,5),data = residuos2,trace = T)##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(0, 0)
## GARCH Model: garch
## Formula Variance: ~ garch(2, 5)
## ARMA Order: 0 0
## Max ARMA Order: 0
## GARCH Order: 2 5
## Max GARCH Order: 5
## Maximum Order: 5
## Conditional Dist: norm
## h.start: 6
## llh.start: 1
## Length of Series: 255
## Recursion Init: mci
## Series Scale: 0.002164843
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -5.43796108 5.437961 0.5437961 TRUE
## omega 0.00000100 100.000000 0.1000000 TRUE
## alpha1 0.00000001 1.000000 0.0500000 TRUE
## alpha2 0.00000001 1.000000 0.0500000 TRUE
## gamma1 -0.99999999 1.000000 0.1000000 FALSE
## gamma2 -0.99999999 1.000000 0.1000000 FALSE
## beta1 0.00000001 1.000000 0.1600000 TRUE
## beta2 0.00000001 1.000000 0.1600000 TRUE
## beta3 0.00000001 1.000000 0.1600000 TRUE
## beta4 0.00000001 1.000000 0.1600000 TRUE
## beta5 0.00000001 1.000000 0.1600000 TRUE
## delta 0.00000000 2.000000 2.0000000 FALSE
## skew 0.10000000 10.000000 1.0000000 FALSE
## shape 1.00000000 10.000000 4.0000000 FALSE
## Index List of Parameters to be Optimized:
## mu omega alpha1 alpha2 beta1 beta2 beta3 beta4 beta5
## 1 2 3 4 7 8 9 10 11
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 358.85856: 0.543796 0.100000 0.0500000 0.0500000 0.160000 0.160000 0.160000 0.160000 0.160000
## 1: 357.87159: 0.543447 0.106148 0.0538157 0.0516416 0.163060 0.163161 0.163147 0.162786 0.162743
## 2: 357.55497: 0.542281 0.110230 0.0558122 0.0471575 0.160074 0.160432 0.160394 0.158949 0.158746
## 3: 348.88002: 0.503527 0.280931 0.164901 1.00000e-08 0.124467 0.130860 0.132941 0.0952450 0.0867086
## 4: 347.79454: 0.443762 0.269468 0.314281 1.00000e-08 0.0767527 0.0517589 0.130356 0.0432213 1.00000e-08
## 5: 337.04478: 0.307531 0.416864 0.558915 1.00000e-08 1.00000e-08 1.00000e-08 0.270088 0.0560437 1.00000e-08
## 6: 336.86319: 0.277697 0.341712 0.647233 1.00000e-08 1.00000e-08 1.00000e-08 0.156802 1.00000e-08 1.00000e-08
## 7: 334.65194: 0.264916 0.368625 0.674213 1.00000e-08 0.00909822 1.00000e-08 0.171047 0.0760328 0.00605687
## 8: 334.31887: 0.262184 0.341091 0.706519 1.00000e-08 1.00000e-08 1.00000e-08 0.0998883 0.0756601 1.00000e-08
## 9: 333.92697: 0.266900 0.416429 0.716520 1.00000e-08 1.00000e-08 1.00000e-08 0.145799 0.0634373 1.00000e-08
## 10: 332.95216: 0.269074 0.402238 0.714527 1.00000e-08 1.00000e-08 1.00000e-08 0.130482 0.0388182 1.00000e-08
## 11: 332.90556: 0.270981 0.398283 0.716233 1.00000e-08 1.00000e-08 1.00000e-08 0.127438 0.0338635 0.00403908
## 12: 332.89270: 0.273475 0.395308 0.720600 1.00000e-08 1.00000e-08 1.00000e-08 0.126768 0.0369569 1.00000e-08
## 13: 332.87067: 0.276886 0.397907 0.724008 1.00000e-08 1.00000e-08 1.00000e-08 0.125049 0.0384811 0.00424035
## 14: 332.84455: 0.278364 0.395379 0.729877 1.00000e-08 1.00000e-08 1.00000e-08 0.127038 0.0332837 0.00290658
## 15: 332.83001: 0.281458 0.397432 0.735329 1.00000e-08 1.00000e-08 1.00000e-08 0.124607 0.0362450 0.00302141
## 16: 332.81898: 0.280790 0.394627 0.743293 1.00000e-08 1.00000e-08 1.00000e-08 0.123176 0.0337692 0.00315022
## 17: 332.81670: 0.280359 0.394435 0.746155 1.00000e-08 1.00000e-08 1.00000e-08 0.124386 0.0348669 0.00488673
## 18: 332.80910: 0.280553 0.395090 0.749096 1.00000e-08 1.00000e-08 1.00000e-08 0.123040 0.0349052 0.00300696
## 19: 332.80533: 0.280168 0.394603 0.752619 1.00000e-08 1.00000e-08 1.00000e-08 0.123067 0.0341845 0.00394211
## 20: 332.79563: 0.277710 0.395243 0.765687 1.00000e-08 1.00000e-08 1.00000e-08 0.116019 0.0356820 0.00386032
## 21: 332.79145: 0.278328 0.399314 0.779611 1.00000e-08 1.00000e-08 1.00000e-08 0.118107 0.0306232 0.00250001
## 22: 332.78478: 0.278312 0.399277 0.779870 1.00000e-08 1.00000e-08 1.00000e-08 0.118178 0.0322054 0.00414316
## 23: 332.78216: 0.277941 0.398120 0.780923 1.00000e-08 1.00000e-08 1.00000e-08 0.117226 0.0326030 0.00300172
## 24: 332.77994: 0.277356 0.397507 0.782305 1.00000e-08 1.00000e-08 1.00000e-08 0.116714 0.0331341 0.00413760
## 25: 332.77818: 0.277002 0.397257 0.784271 1.00000e-08 1.00000e-08 1.00000e-08 0.115887 0.0331272 0.00364376
## 26: 332.77696: 0.277028 0.397718 0.786386 1.00000e-08 1.00000e-08 1.00000e-08 0.115247 0.0334458 0.00392455
## 27: 332.77198: 0.271632 0.396176 0.799489 1.00000e-08 1.00000e-08 1.00000e-08 0.111506 0.0329578 0.00493461
## 28: 332.76584: 0.269438 0.398631 0.815015 1.00000e-08 1.00000e-08 1.00000e-08 0.106740 0.0327755 0.00364247
## 29: 332.76052: 0.268990 0.400620 0.830195 1.00000e-08 1.00000e-08 1.00000e-08 0.0996298 0.0321963 0.00499340
## 30: 332.75958: 0.268901 0.401334 0.830453 1.00000e-08 1.00000e-08 1.00000e-08 0.100392 0.0325560 0.00512105
## 31: 332.75898: 0.268677 0.401528 0.831383 1.00000e-08 1.00000e-08 1.00000e-08 0.100227 0.0322476 0.00475452
## 32: 332.75840: 0.268206 0.402075 0.833414 1.00000e-08 1.00000e-08 1.00000e-08 0.100033 0.0320654 0.00502228
## 33: 332.75622: 0.265070 0.403451 0.847857 1.00000e-08 1.00000e-08 1.00000e-08 0.0957139 0.0314597 0.00523018
## 34: 332.75522: 0.262791 0.405128 0.862955 1.00000e-08 1.00000e-08 1.00000e-08 0.0919163 0.0311553 0.00526587
## 35: 332.75517: 0.261394 0.406347 0.868108 1.00000e-08 1.00000e-08 1.00000e-08 0.0898674 0.0307170 0.00535114
## 36: 332.75512: 0.261418 0.406024 0.868688 1.00000e-08 1.00000e-08 1.00000e-08 0.0898821 0.0308906 0.00538611
## 37: 332.75512: 0.261481 0.406006 0.868535 1.00000e-08 1.00000e-08 1.00000e-08 0.0899648 0.0308775 0.00537789
## 38: 332.75512: 0.261473 0.406015 0.868538 1.00000e-08 1.00000e-08 1.00000e-08 0.0899517 0.0308808 0.00537769
##
## Final Estimate of the Negative LLH:
## LLH: -1231.774 norm LLH: -4.830485
## mu omega alpha1 alpha2 beta1 beta2
## 5.660472e-04 1.902810e-06 8.685377e-01 1.000000e-08 1.000000e-08 1.000000e-08
## beta3 beta4 beta5
## 8.995167e-02 3.088079e-02 5.377694e-03
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu omega alpha1 alpha2 beta1
## mu -7.510089e+07 4.586798e+09 -1.220668e+04 7.115439e+03 1.862629e+04
## omega 4.586798e+09 -2.181932e+13 -7.067350e+06 -1.538738e+07 -6.421650e+07
## alpha1 -1.220668e+04 -7.067350e+06 -3.322676e+01 -5.186343e+01 -1.003544e+02
## alpha2 7.115439e+03 -1.538738e+07 -5.186343e+01 1.254035e+03 9.386402e+02
## beta1 1.862629e+04 -6.421650e+07 -1.003544e+02 9.386402e+02 5.451629e+02
## beta2 1.948559e+04 -3.762525e+07 -1.196314e+02 -1.536160e+02 -2.615660e+02
## beta3 6.407348e+04 -6.601156e+07 -8.540201e+01 -3.713053e+02 -5.046432e+02
## beta4 4.546461e+04 -6.770344e+07 -1.088175e+02 -2.328607e+02 -5.302779e+02
## beta5 -2.484877e+04 -1.014531e+08 -5.203438e+01 -1.622732e+02 -5.192082e+02
## beta2 beta3 beta4 beta5
## mu 1.948559e+04 6.407348e+04 4.546461e+04 -2.484877e+04
## omega -3.762525e+07 -6.601156e+07 -6.770344e+07 -1.014531e+08
## alpha1 -1.196314e+02 -8.540201e+01 -1.088175e+02 -5.203438e+01
## alpha2 -1.536160e+02 -3.713053e+02 -2.328607e+02 -1.622732e+02
## beta1 -2.615660e+02 -5.046432e+02 -5.302779e+02 -5.192082e+02
## beta2 1.786575e+03 -2.008473e+02 -2.620292e+02 -1.019291e+03
## beta3 -2.008473e+02 -4.699874e+02 -4.154780e+02 -4.709219e+02
## beta4 -2.620292e+02 -4.154780e+02 -1.944674e+03 -7.828807e+02
## beta5 -1.019291e+03 -4.709219e+02 -7.828807e+02 -3.991743e+03
## attr(,"time")
## Time difference of 0.05500293 secs
##
## --- END OF TRACE ---## Warning in sqrt(diag(fit$cvar)): Se han producido NaNs##
## Time to Estimate Parameters:
## Time difference of 0.1360061 secssummary(modelo2)##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(2, 5), data = residuos2, trace = T)
##
## Mean and Variance Equation:
## data ~ garch(2, 5)
## <environment: 0x000000001d0479b0>
## [data = residuos2]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 alpha2 beta1 beta2
## 5.6605e-04 1.9028e-06 8.6854e-01 1.0000e-08 1.0000e-08 1.0000e-08
## beta3 beta4 beta5
## 8.9952e-02 3.0881e-02 5.3777e-03
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 5.660e-04 1.257e-04 4.504 6.66e-06 ***
## omega 1.903e-06 NA NA NA
## alpha1 8.685e-01 NA NA NA
## alpha2 1.000e-08 NA NA NA
## beta1 1.000e-08 NA NA NA
## beta2 1.000e-08 NA NA NA
## beta3 8.995e-02 6.981e-02 1.288 0.198
## beta4 3.088e-02 2.675e-02 1.154 0.248
## beta5 5.378e-03 1.605e-02 0.335 0.738
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 1231.774 normalized: 4.830485
##
## Description:
## Thu Jul 23 16:50:15 2020 by user: daffy
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 4419.944 0
## Shapiro-Wilk Test R W 0.5891052 0
## Ljung-Box Test R Q(10) 19.62788 0.0329754
## Ljung-Box Test R Q(15) 20.91272 0.1396413
## Ljung-Box Test R Q(20) 21.15415 0.3881099
## Ljung-Box Test R^2 Q(10) 1.61698 0.9985225
## Ljung-Box Test R^2 Q(15) 3.033179 0.9995694
## Ljung-Box Test R^2 Q(20) 3.780567 0.9999708
## LM Arch Test R TR^2 2.675193 0.997435
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -9.590382 -9.465396 -9.592762 -9.540108modelo3<-garchFit(~garch(1,0),data = residuos2,trace = T)##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(0, 0)
## GARCH Model: garch
## Formula Variance: ~ garch(1, 0)
## ARMA Order: 0 0
## Max ARMA Order: 0
## GARCH Order: 1 0
## Max GARCH Order: 1
## Maximum Order: 1
## Conditional Dist: norm
## h.start: 2
## llh.start: 1
## Length of Series: 255
## Recursion Init: mci
## Series Scale: 0.002164843
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -5.43796108 5.437961 0.5437961 TRUE
## omega 0.00000100 100.000000 0.1000000 TRUE
## alpha1 0.00000001 1.000000 0.1000000 TRUE
## gamma1 -0.99999999 1.000000 0.1000000 FALSE
## delta 0.00000000 2.000000 2.0000000 FALSE
## skew 0.10000000 10.000000 1.0000000 FALSE
## shape 1.00000000 10.000000 4.0000000 FALSE
## Index List of Parameters to be Optimized:
## mu omega alpha1
## 1 2 3
## Persistence: 0.1
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 795.47308: 0.543796 0.100000 0.100000
## 1: 355.04218: 0.530870 1.06839 0.348310
## 2: 351.50125: 0.266658 1.02329 0.457395
## 3: 345.07443: 0.192659 0.856893 1.00000
## 4: 342.49367: 0.307253 0.810028 1.00000
## 5: 340.32963: 0.308108 0.752647 1.00000
## 6: 334.68672: 0.278555 0.529998 0.986080
## 7: 334.15165: 0.218520 0.494889 1.00000
## 8: 334.13356: 0.220896 0.520892 1.00000
## 9: 334.11067: 0.225210 0.511059 1.00000
## 10: 334.11047: 0.224118 0.510224 1.00000
## 11: 334.11046: 0.224259 0.510345 1.00000
## 12: 334.11046: 0.224260 0.510345 1.00000
##
## Final Estimate of the Negative LLH:
## LLH: -1230.418 norm LLH: -4.82517
## mu omega alpha1
## 4.854875e-04 2.391756e-06 1.000000e+00
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu omega alpha1
## mu -82891027.36 7.554743e+09 -1.764294e+04
## omega 7554743130.23 -1.533268e+13 -5.775449e+06
## alpha1 -17642.94 -5.775449e+06 -2.183722e+01
## attr(,"time")
## Time difference of 0.008008003 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.02999997 secssummary(modelo3)##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 0), data = residuos2, trace = T)
##
## Mean and Variance Equation:
## data ~ garch(1, 0)
## <environment: 0x000000001c1bd080>
## [data = residuos2]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1
## 4.8549e-04 2.3918e-06 1.0000e+00
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 4.855e-04 1.315e-04 3.692 0.000223 ***
## omega 2.392e-06 2.932e-07 8.156 4.44e-16 ***
## alpha1 1.000e+00 2.639e-01 3.789 0.000151 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 1230.418 normalized: 4.82517
##
## Description:
## Thu Jul 23 16:50:15 2020 by user: daffy
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 3442.491 0
## Shapiro-Wilk Test R W 0.5869282 0
## Ljung-Box Test R Q(10) 22.96062 0.01089288
## Ljung-Box Test R Q(15) 24.3535 0.05932849
## Ljung-Box Test R Q(20) 24.63026 0.2159442
## Ljung-Box Test R^2 Q(10) 4.257838 0.9349667
## Ljung-Box Test R^2 Q(15) 6.031047 0.9792215
## Ljung-Box Test R^2 Q(20) 7.912376 0.9924318
## LM Arch Test R TR^2 5.349967 0.9452573
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -9.626811 -9.585149 -9.627083 -9.610053modelo4<-garchFit(~garch(2,0),data = residuos2,trace = T)##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(0, 0)
## GARCH Model: garch
## Formula Variance: ~ garch(2, 0)
## ARMA Order: 0 0
## Max ARMA Order: 0
## GARCH Order: 2 0
## Max GARCH Order: 2
## Maximum Order: 2
## Conditional Dist: norm
## h.start: 3
## llh.start: 1
## Length of Series: 255
## Recursion Init: mci
## Series Scale: 0.002164843
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -5.43796108 5.437961 0.5437961 TRUE
## omega 0.00000100 100.000000 0.1000000 TRUE
## alpha1 0.00000001 1.000000 0.0500000 TRUE
## alpha2 0.00000001 1.000000 0.0500000 TRUE
## gamma1 -0.99999999 1.000000 0.1000000 FALSE
## gamma2 -0.99999999 1.000000 0.1000000 FALSE
## delta 0.00000000 2.000000 2.0000000 FALSE
## skew 0.10000000 10.000000 1.0000000 FALSE
## shape 1.00000000 10.000000 4.0000000 FALSE
## Index List of Parameters to be Optimized:
## mu omega alpha1 alpha2
## 1 2 3 4
## Persistence: 0.1
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 771.16190: 0.543796 0.100000 0.0500000 0.0500000
## 1: 358.86014: 0.532960 1.00613 0.361643 0.335326
## 2: 353.94372: 0.263358 0.989628 0.400630 0.286207
## 3: 346.76526: 0.143362 0.506805 1.00000 1.00000
## 4: 343.79113: 0.263967 0.457723 1.00000 0.975928
## 5: 342.95770: 0.276257 0.521212 1.00000 0.756127
## 6: 341.86648: 0.276679 0.558907 1.00000 0.538949
## 7: 335.92006: 0.272499 0.604127 1.00000 1.00000e-08
## 8: 335.79177: 0.261008 0.603179 1.00000 1.00000e-08
## 9: 335.42963: 0.233238 0.588889 1.00000 1.00000e-08
## 10: 335.03509: 0.212895 0.559452 1.00000 1.00000e-08
## 11: 334.70631: 0.207083 0.516647 1.00000 1.00000e-08
## 12: 334.64231: 0.218573 0.510433 1.00000 1.00000e-08
## 13: 334.63459: 0.225148 0.512478 1.00000 1.00000e-08
## 14: 334.63457: 0.225045 0.512175 1.00000 1.00000e-08
## 15: 334.63457: 0.225043 0.512191 1.00000 1.00000e-08
## 16: 334.63457: 0.225043 0.512191 1.00000 1.00000e-08
##
## Final Estimate of the Negative LLH:
## LLH: -1229.894 norm LLH: -4.823115
## mu omega alpha1 alpha2
## 4.871828e-04 2.400409e-06 1.000000e+00 1.000000e-08
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu omega alpha1 alpha2
## mu -82216931.93 7.471745e+09 -1.764285e+04 1.787917e+04
## omega 7471745107.92 -1.519656e+13 -5.693638e+06 -1.888723e+07
## alpha1 -17642.85 -5.693638e+06 -2.149857e+01 -3.793005e+01
## alpha2 17879.17 -1.888723e+07 -3.793005e+01 7.593479e+02
## attr(,"time")
## Time difference of 0.007987976 secs
##
## --- END OF TRACE ---## Warning in sqrt(diag(fit$cvar)): Se han producido NaNs##
## Time to Estimate Parameters:
## Time difference of 0.02900195 secssummary(modelo4)##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(2, 0), data = residuos2, trace = T)
##
## Mean and Variance Equation:
## data ~ garch(2, 0)
## <environment: 0x000000001cc28d48>
## [data = residuos2]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 alpha2
## 4.8718e-04 2.4004e-06 1.0000e+00 1.0000e-08
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 4.872e-04 1.302e-04 3.742 0.000182 ***
## omega 2.400e-06 2.947e-07 8.144 4.44e-16 ***
## alpha1 1.000e+00 2.545e-01 3.930 8.51e-05 ***
## alpha2 1.000e-08 NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 1229.894 normalized: 4.823115
##
## Description:
## Thu Jul 23 16:50:15 2020 by user: daffy
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 3438.372 0
## Shapiro-Wilk Test R W 0.5869367 0
## Ljung-Box Test R Q(10) 23.01554 0.01068938
## Ljung-Box Test R Q(15) 24.40587 0.05851392
## Ljung-Box Test R Q(20) 24.68229 0.2138573
## Ljung-Box Test R^2 Q(10) 4.262055 0.9347518
## Ljung-Box Test R^2 Q(15) 6.042036 0.979033
## Ljung-Box Test R^2 Q(20) 7.919836 0.9923849
## LM Arch Test R TR^2 5.359499 0.9448816
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -9.614857 -9.559308 -9.615339 -9.592513