Foreign Financial Commercial Paper Outstanding
Hernan Perci Nuñez Palomino - Rodney Niles Guerrero Fernandez
Última edición 08 Enero 2022
1 Librerias
library(readr)
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: fBasicslibrary('lmtest')## Loading required package: zoo##
## Attaching package: 'zoo'## The following object is masked from 'package:timeSeries':
##
## time<-## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary('lmtest')
library('FinTS')
library('fGarch')
library('forecast')##
## Attaching package: 'forecast'## The following object is masked from 'package:FinTS':
##
## Acflibrary('TSA')## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast##
## Attaching package: 'TSA'## The following objects are masked from 'package:timeDate':
##
## kurtosis, skewness## The following object is masked from 'package:readr':
##
## spec## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tar2 Datos
data <- read_csv("FFINCP.csv")## Rows: 1097 Columns: 2## -- Column specification --------------------------------------------------------
## Delimiter: ","
## dbl (1): FFINCP
## date (1): DATE##
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.#Transformación de los Datos en un Objeto Serie de Tiempo
data_ts <- ts(data$FFINCP)3 Estadística descriptiva de la Serie de Tiempo
plot.ts(data_ts,main = 'Foreign Financial Commercial Paper Outstanding', xlab = 'Tiempo', ylab = 'data_ts')
summary(data_ts)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 72.28 150.45 217.50 214.46 267.71 503.40Indicios de heterocedasticidad Se estudiara la serie de retornos
#Calculo de Retornos
ret <- diff(log(data_ts))*100
plot.ts(ret,main = 'Retornos St. Louis Fed Financial Stress Index', xlab = 'Tiempo', ylab = 'Ret')
mayor dispersion entre 400 y 600
#Estadísticos descriptivos
summary(ret)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -21.4884 -1.3253 0.1989 0.1256 1.6805 15.3790retorno promedio de 0.12% retorno maximo 15.37%
4 Análisis de la serie de rendimientos, prueba de raíces unitarias.
adf.test(ret) # p-value < 0.05 => no unit-root## Warning in adf.test(ret): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: ret
## Dickey-Fuller = -10.096, Lag order = 10, p-value = 0.01
## alternative hypothesis: stationaryla serie de retornos es estacionario
5 Estimación del modelo ARIMA
5.1 Identificación
5.1.1 Función de Auto-correlaciones
acf(ret)
pacf(ret)
p 1,2 q 1,2,3
# Modelo ARIMA(1,0,1)
ModeloArima101 <- arima(ret,c(1,0,1)) # -->> ARMA(1,1)
coeftest(ModeloArima101)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.663610 0.064367 10.3098 < 2.2e-16 ***
## ma1 -0.482686 0.073213 -6.5929 4.314e-11 ***
## intercept 0.120889 0.141300 0.8555 0.3923
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo ARIMA(1,1,1)
ModeloArima111 <- arima(ret,c(1,1,1)) # -->> ARIMA(1,1,1)
coeftest(ModeloArima111)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.1851864 0.0298103 6.2122 5.226e-10 ***
## ma1 -0.9999995 0.0028222 -354.3293 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo ARIMA(1,0,2)
ModeloArima102 <- arima(ret,c(1,0,2)) # -->> ARMA(1,2)
coeftest(ModeloArima102)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.431312 0.119194 3.6186 0.0002962 ***
## ma1 -0.284401 0.119384 -2.3822 0.0172077 *
## ma2 0.133768 0.037379 3.5787 0.0003453 ***
## intercept 0.120992 0.136576 0.8859 0.3756757
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo ARIMA(1,1,2)
ModeloArima112 <- arima(ret,c(1,1,2)) # -->> ARIMA(1,1,2)
coeftest(ModeloArima112)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.665316 0.063489 10.4793 < 2.2e-16 ***
## ma1 -1.482801 0.072136 -20.5556 < 2.2e-16 ***
## ma2 0.482806 0.072087 6.6976 2.119e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo ARIMA(1,0,3)
ModeloArima103 <- arima(ret,c(1,0,3)) # -->> ARMA(1,3)
coeftest(ModeloArima103)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.395068 0.240525 1.6425 0.100481
## ma1 -0.247894 0.241544 -1.0263 0.304755
## ma2 0.137752 0.043891 3.1385 0.001698 **
## ma3 0.010592 0.058904 0.1798 0.857296
## intercept 0.121111 0.136116 0.8898 0.373596
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo ARIMA(1,1,3)
ModeloArima113 <- arima(ret,c(1,1,3)) # -->> ARIMA(1,1,3)
coeftest(ModeloArima113)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.437790 0.116645 3.7532 0.0001746 ***
## ma1 -1.290390 0.116889 -11.0394 < 2.2e-16 ***
## ma2 0.423982 0.102688 4.1289 3.646e-05 ***
## ma3 -0.133593 0.037201 -3.5911 0.0003293 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo ARIMA(2,0,1)
ModeloArima201 <- arima(ret,c(2,0,1)) # -->> ARMA(2,1)
coeftest(ModeloArima201)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.25713 0.14668 1.7530 0.07961 .
## ar2 0.15645 0.04177 3.7455 0.00018 ***
## ma1 -0.10897 0.14766 -0.7380 0.46052
## intercept 0.12300 0.13897 0.8851 0.37612
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo ARIMA(2,1,1)
ModeloArima211 <- arima(ret,c(2,1,1)) # -->> ARIMA(2,1,1)
coeftest(ModeloArima211)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.1525878 0.0298604 5.1100 3.221e-07 ***
## ar2 0.1767687 0.0298539 5.9211 3.197e-09 ***
## ma1 -0.9999999 0.0026799 -373.1484 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo ARIMA(2,0,2)
ModeloArima202 <- arima(ret,c(2,0,2)) # -->> ARMA(2,2)
coeftest(ModeloArima202)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.493462 0.346226 1.4253 0.1541
## ar2 -0.049603 0.252743 -0.1963 0.8444
## ma1 -0.346212 0.343877 -1.0068 0.3140
## ma2 0.172326 0.196930 0.8751 0.3815
## intercept 0.121348 0.135836 0.8933 0.3717# Modelo ARIMA(2,1,2)
ModeloArima212 <- arima(ret,c(2,1,2)) # -->> ARIMA(2,1,2)
coeftest(ModeloArima212)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.263693 0.144766 1.8215 0.0685294 .
## ar2 0.156457 0.041789 3.7440 0.0001811 ***
## ma1 -1.114571 0.145659 -7.6519 1.98e-14 ***
## ma2 0.114572 0.145632 0.7867 0.4314460
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo ARIMA(2,0,3)
ModeloArima203 <- arima(ret,c(2,0,3)) # -->> ARMA(2,3)
coeftest(ModeloArima203)## Warning in sqrt(diag(se)): Se han producido NaNs##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.102871 NaN NaN NaN
## ar2 0.137805 NaN NaN NaN
## ma1 0.044088 NaN NaN NaN
## ma2 0.043860 NaN NaN NaN
## ma3 0.045423 NaN NaN NaN
## intercept 0.121188 0.136490 0.8879 0.3746# Modelo ARIMA(2,1,3)
ModeloArima213 <- arima(ret,c(2,1,3)) # -->> ARIMA(2,1,3)
coeftest(ModeloArima213)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.483504 0.335133 1.4427 0.1491
## ar2 -0.036841 0.248150 -0.1485 0.8820
## ma1 -1.335188 0.333176 -4.0074 6.138e-05 ***
## ma2 0.497210 0.513180 0.9689 0.3326
## ma3 -0.162022 0.194645 -0.8324 0.4052
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 TablaDiagnosticoArima <-
rbind.data.frame(
list('ModeloArima101' ,
all(coeftest(ModeloArima101)[,4] <=
0.05),AIC(ModeloArima101)),
list('ModeloArima111' ,
all(coeftest(ModeloArima111)[,4] <=
0.05),AIC(ModeloArima111)),
list('ModeloArima102' ,
all(coeftest(ModeloArima102)[,4] <=
0.05),AIC(ModeloArima102)),
list('ModeloArima112' ,
all(coeftest(ModeloArima112)[,4] <=
0.05),AIC(ModeloArima112)),
list('ModeloArima103' ,
all(coeftest(ModeloArima103)[,4] <=
0.05),AIC(ModeloArima103)),
list('ModeloArima113' ,
all(coeftest(ModeloArima113)[,4] <=
0.05),AIC(ModeloArima113)),
list('ModeloArima201' ,
all(coeftest(ModeloArima201)[,4] <=
0.05),AIC(ModeloArima201)),
list('ModeloArima211' ,
all(coeftest(ModeloArima211)[,4] <=
0.05),AIC(ModeloArima211)),
list('ModeloArima202' ,
all(coeftest(ModeloArima202)[,4] <=
0.05),AIC(ModeloArima202)),
list('ModeloArima212' ,
all(coeftest(ModeloArima212)[,4] <=
0.05),AIC(ModeloArima212)),
list('ModeloArima203' ,
all(coeftest(ModeloArima203)[,4] <=
0.05),AIC(ModeloArima203)),
list('ModeloArima213' ,
all(coeftest(ModeloArima213)[,4] <=
0.05),AIC(ModeloArima213))
)## Warning in sqrt(diag(se)): Se han producido NaNs names(TablaDiagnosticoArima) <-
c('Modelo','AllCoef<0.05?','AIC')
TablaDiagnosticoArima <- TablaDiagnosticoArima[order(-
TablaDiagnosticoArima$`AllCoef<0.05`,TablaDiagnosticoArima$
AIC),]
head(TablaDiagnosticoArima)| Modelo | AllCoef<0.05? | AIC | |
|---|---|---|---|
| 8 | ModeloArima211 | TRUE | 5551.267 |
| 6 | ModeloArima113 | TRUE | 5552.014 |
| 4 | ModeloArima112 | TRUE | 5560.985 |
| 2 | ModeloArima111 | TRUE | 5583.777 |
| 3 | ModeloArima102 | FALSE | 5549.875 |
| 7 | ModeloArima201 | FALSE | 5550.605 |
coeftest(ModeloArima211)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.1525878 0.0298604 5.1100 3.221e-07 ***
## ar2 0.1767687 0.0298539 5.9211 3.197e-09 ***
## ma1 -0.9999999 0.0026799 -373.1484 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ModeloArimaElegido <- ModeloArima2116 Validación
par(mfrow=c(2,2))
plot.ts(residuals(ModeloArimaElegido),main = 'Residuos,
Modelo en Media Elegido, Arima211')
qqnorm(residuals(ModeloArimaElegido))
qqline(residuals(ModeloArimaElegido))
acf(residuals(ModeloArimaElegido),na.action = na.omit)
pacf(residuals(ModeloArimaElegido),na.action = na.omit)
7 Análisis de los efectos GARCH
Box.test(residuals(ModeloArimaElegido)^2,type = 'Ljung-Box',lag = 12)##
## Box-Ljung test
##
## data: residuals(ModeloArimaElegido)^2
## X-squared = 40.911, df = 12, p-value = 5.071e-05 ArchTest(residuals(ModeloArimaElegido),lag = 5)##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: residuals(ModeloArimaElegido)
## Chi-squared = 23.085, df = 5, p-value = 0.0003252Los errores estan correlacionados entre si. Por tanto es necesario estimar garch.
Los errores tienen efectos garch significativos. Se necesita modelo garch.
8 Estimación del modelo GARCH
8.1 Correlogramas y Gráfico, Autocorrelaciones Simples y Parciales de la Serie de Residuos
par(mfrow=c(2,2))
acf(residuals(ModeloArimaElegido),na.action = na.omit)
pacf(residuals(ModeloArimaElegido),na.action = na.omit)
acf(residuals(ModeloArimaElegido)^2,na.action = na.omit)
pacf(residuals(ModeloArimaElegido)^2,na.action = na.omit)
8.2 Modelos Plausibles
ModeloGarch11 <-
garch(na.omit(residuals(ModeloArimaElegido)),order =
c(1,1),na.action=na.omit)##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 8.275202e+00 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 1.748e+03
## 1 3 1.744e+03 2.34e-03 7.78e-03 6.0e-03 1.4e+03 1.0e-01 5.30e+00
## 2 5 1.743e+03 2.60e-04 2.72e-04 5.6e-04 1.1e+01 1.0e-02 5.57e-01
## 3 7 1.742e+03 3.65e-04 3.65e-04 1.1e-03 2.0e+00 2.0e-02 1.43e-02
## 4 9 1.742e+03 5.01e-05 5.02e-05 2.4e-04 8.8e+00 4.0e-03 1.28e-02
## 5 11 1.742e+03 7.96e-05 7.97e-05 4.8e-04 2.0e+00 8.0e-03 6.77e-03
## 6 14 1.742e+03 1.33e-06 1.33e-06 9.4e-06 1.4e+02 1.6e-04 5.23e-03
## 7 16 1.742e+03 2.64e-06 2.64e-06 1.9e-05 1.8e+01 3.2e-04 2.91e-03
## 8 19 1.742e+03 5.24e-08 5.24e-08 3.7e-07 3.4e+03 6.4e-06 2.87e-03
## 9 21 1.742e+03 1.05e-07 1.05e-07 7.5e-07 4.3e+02 1.3e-05 2.80e-03
## 10 23 1.742e+03 2.09e-08 2.09e-08 1.5e-07 8.6e+03 2.6e-06 2.80e-03
## 11 25 1.742e+03 4.18e-08 4.18e-08 3.0e-07 1.1e+03 5.1e-06 2.79e-03
## 12 27 1.742e+03 8.37e-09 8.37e-09 6.0e-08 2.1e+04 1.0e-06 2.79e-03
## 13 30 1.742e+03 6.69e-08 6.69e-08 4.8e-07 6.7e+02 8.2e-06 2.79e-03
## 14 33 1.742e+03 1.34e-09 1.34e-09 9.6e-09 1.3e+05 1.6e-07 2.79e-03
## 15 35 1.742e+03 2.68e-09 2.68e-09 1.9e-08 1.7e+04 3.3e-07 2.79e-03
## 16 39 1.742e+03 5.35e-12 5.35e-12 3.8e-11 6.8e-01 6.6e-10 -2.02e-03
## 17 41 1.742e+03 1.07e-11 1.07e-11 7.7e-11 6.8e-01 1.3e-09 -2.02e-03
## 18 43 1.742e+03 2.14e-11 2.14e-11 1.5e-10 6.8e-01 2.6e-09 -2.02e-03
## 19 46 1.742e+03 4.28e-13 4.28e-13 3.1e-12 6.8e-01 5.2e-11 -2.02e-03
## 20 48 1.742e+03 8.58e-13 8.56e-13 6.1e-12 6.8e-01 1.0e-10 -2.01e-03
## 21 50 1.742e+03 1.70e-13 1.71e-13 1.2e-12 6.8e-01 2.1e-11 -2.02e-03
## 22 52 1.742e+03 3.43e-13 3.43e-13 2.5e-12 6.8e-01 4.2e-11 -2.01e-03
## 23 54 1.742e+03 6.84e-13 6.85e-13 4.9e-12 6.8e-01 8.4e-11 -2.02e-03
## 24 56 1.742e+03 1.37e-13 1.37e-13 9.8e-13 6.8e-01 1.7e-11 -2.02e-03
## 25 58 1.742e+03 2.98e-14 2.74e-14 2.0e-13 6.8e-01 3.4e-12 -2.01e-03
## 26 60 1.742e+03 6.26e-15 5.48e-15 3.9e-14 6.8e-01 6.7e-13 -2.01e-03
## 27 62 1.742e+03 -3.92e-16 1.10e-15 7.9e-15 6.8e-01 1.3e-13 -2.02e-03
##
## ***** FALSE CONVERGENCE *****
##
## FUNCTION 1.742242e+03 RELDX 7.860e-15
## FUNC. EVALS 62 GRAD. EVALS 27
## PRELDF 1.096e-15 NPRELDF -2.017e-03
##
## I FINAL X(I) D(I) G(I)
##
## 1 8.267843e+00 1.000e+00 2.954e+00
## 2 1.395996e-01 1.000e+00 -1.970e+00
## 3 1.004897e-12 1.000e+00 1.378e+01 ModeloGarch02 <-
garch(na.omit(residuals(ModeloArimaElegido)),order =
c(0,2),na.action=na.omit)##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 8.275202e+00 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 1.744e+03
## 1 4 1.742e+03 1.12e-03 8.64e-03 7.5e-03 9.7e+02 1.2e-01 4.19e+00
## 2 6 1.741e+03 3.14e-04 2.97e-04 5.7e-04 4.6e+00 1.2e-02 1.36e-01
## 3 7 1.740e+03 4.21e-04 4.45e-04 1.2e-03 3.3e+00 2.5e-02 1.86e-02
## 4 8 1.740e+03 4.49e-05 3.02e-04 2.6e-03 2.0e+00 5.0e-02 2.01e-02
## 5 9 1.740e+03 1.99e-04 2.74e-04 2.4e-03 2.0e+00 5.0e-02 1.01e-02
## 6 11 1.740e+03 1.68e-05 6.81e-05 9.5e-04 3.1e+00 1.8e-02 6.89e-03
## 7 12 1.740e+03 4.77e-05 5.53e-05 8.8e-04 2.0e+00 1.8e-02 5.16e-03
## 8 13 1.740e+03 3.73e-05 4.05e-05 9.7e-04 2.0e+00 1.8e-02 4.55e-03
## 9 17 1.738e+03 1.10e-03 1.94e-03 6.4e-02 9.3e-01 9.8e-01 4.31e-03
## 10 19 1.738e+03 3.76e-05 3.23e-04 6.1e-03 1.8e+00 9.8e-02 2.43e-03
## 11 20 1.738e+03 1.20e-05 9.11e-05 6.7e-03 1.2e+00 9.8e-02 9.97e-05
## 12 22 1.738e+03 4.43e-05 9.94e-05 2.8e-03 1.5e+00 4.5e-02 1.08e-04
## 13 23 1.738e+03 1.88e-05 2.23e-05 1.1e-03 0.0e+00 1.9e-02 2.23e-05
## 14 24 1.738e+03 5.60e-07 6.33e-07 1.1e-04 0.0e+00 2.5e-03 6.33e-07
## 15 25 1.738e+03 2.28e-08 2.44e-08 3.4e-05 0.0e+00 6.2e-04 2.44e-08
## 16 26 1.738e+03 1.55e-10 1.58e-10 2.5e-06 0.0e+00 4.5e-05 1.58e-10
## 17 27 1.738e+03 7.77e-14 7.78e-14 6.8e-08 0.0e+00 1.2e-06 7.78e-14
##
## ***** RELATIVE FUNCTION CONVERGENCE *****
##
## FUNCTION 1.737581e+03 RELDX 6.850e-08
## FUNC. EVALS 27 GRAD. EVALS 18
## PRELDF 7.777e-14 NPRELDF 7.777e-14
##
## I FINAL X(I) D(I) G(I)
##
## 1 7.141701e+00 1.000e+00 1.626e-07
## 2 1.543825e-01 1.000e+00 -4.395e-06
## 3 8.387965e-02 1.000e+00 5.517e-06 ModeloGarch22 <-
garch(na.omit(residuals(ModeloArimaElegido)),order =
c(2,2),na.action=na.omit)##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 7.355735e+00 1.000e+00
## 2 5.000000e-02 1.000e+00
## 3 5.000000e-02 1.000e+00
## 4 5.000000e-02 1.000e+00
## 5 5.000000e-02 1.000e+00
##
## IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
## 0 1 1.743e+03
## 1 3 1.740e+03 2.11e-03 6.87e-03 6.7e-03 1.2e+03 1.0e-01 4.12e+00
## 2 5 1.739e+03 3.79e-04 4.16e-04 4.5e-04 1.3e+01 1.0e-02 1.40e+00
## 3 6 1.738e+03 4.39e-04 4.38e-04 9.4e-04 2.5e+00 2.0e-02 8.07e-02
## 4 8 1.738e+03 5.11e-05 5.14e-05 2.1e-04 8.9e+00 4.0e-03 9.51e-02
## 5 10 1.738e+03 8.48e-05 8.51e-05 4.0e-04 2.1e+00 8.0e-03 5.22e-02
## 6 12 1.738e+03 1.53e-05 1.54e-05 6.8e-05 4.7e+01 1.6e-03 3.32e-02
## 7 14 1.738e+03 2.91e-05 2.91e-05 1.3e-04 4.9e+00 3.2e-03 1.81e-03
## 8 16 1.738e+03 5.26e-05 5.26e-05 2.7e-04 2.9e+00 6.4e-03 1.38e-03
## 9 18 1.738e+03 9.66e-06 9.66e-06 5.6e-05 3.5e+01 1.3e-03 7.99e-04
## 10 20 1.738e+03 1.90e-06 1.90e-06 1.1e-05 1.7e+02 2.6e-04 3.17e-04
## 11 22 1.738e+03 3.78e-07 3.78e-07 2.2e-06 8.4e+02 5.1e-05 3.04e-04
## 12 24 1.738e+03 7.56e-08 7.56e-08 4.5e-07 4.2e+03 1.0e-05 3.02e-04
## 13 27 1.738e+03 6.04e-07 6.04e-07 3.6e-06 1.3e+02 8.2e-05 3.01e-04
## 14 30 1.738e+03 1.21e-08 1.21e-08 7.2e-08 2.6e+04 1.6e-06 3.01e-04
## 15 32 1.738e+03 2.42e-09 2.42e-09 1.4e-08 1.3e+05 3.3e-07 3.00e-04
## 16 35 1.738e+03 4.83e-11 4.83e-11 2.9e-10 6.5e+06 6.6e-09 3.00e-04
## 17 37 1.738e+03 9.66e-11 9.66e-11 5.7e-10 8.2e+05 1.3e-08 3.00e-04
## 18 39 1.738e+03 1.93e-11 1.93e-11 1.1e-10 1.6e+07 2.6e-09 3.00e-04
## 19 41 1.738e+03 3.86e-11 3.86e-11 2.3e-10 2.0e+06 5.2e-09 3.00e-04
## 20 43 1.738e+03 7.73e-12 7.73e-12 4.6e-11 4.1e+07 1.0e-09 3.00e-04
## 21 45 1.738e+03 1.55e-11 1.55e-11 9.2e-11 5.1e+06 2.1e-09 3.00e-04
## 22 47 1.738e+03 3.09e-11 3.09e-11 1.8e-10 2.6e+06 4.2e-09 3.00e-04
## 23 50 1.738e+03 6.19e-13 6.18e-13 3.7e-12 5.1e+08 8.4e-11 3.00e-04
## 24 52 1.738e+03 1.24e-12 1.24e-12 7.3e-12 6.4e+07 1.7e-10 3.00e-04
## 25 54 1.738e+03 2.46e-13 2.47e-13 1.5e-12 1.3e+09 3.4e-11 3.00e-04
## 26 56 1.738e+03 4.94e-13 4.95e-13 2.9e-12 1.6e+08 6.7e-11 3.00e-04
## 27 58 1.738e+03 1.00e-13 9.89e-14 5.9e-13 3.2e+09 1.3e-11 3.00e-04
## 28 61 1.738e+03 7.91e-13 7.91e-13 4.7e-12 1.0e+08 1.1e-10 3.00e-04
## 29 64 1.738e+03 1.66e-14 1.58e-14 9.4e-14 2.0e+10 2.1e-12 3.00e-04
## 30 66 1.738e+03 3.15e-14 3.17e-14 1.9e-13 2.5e+09 4.3e-12 2.99e-04
## 31 68 1.738e+03 6.02e-15 6.33e-15 3.8e-14 5.0e+10 8.6e-13 3.00e-04
## 32 70 1.738e+03 1.22e-14 1.27e-14 7.5e-14 6.2e+09 1.7e-12 3.01e-04
## 33 72 1.738e+03 3.14e-15 2.53e-15 1.5e-14 1.2e+11 3.4e-13 2.99e-04
## 34 74 1.738e+03 5.10e-15 5.06e-15 3.0e-14 1.6e+10 6.9e-13 3.00e-04
## 35 76 1.738e+03 -3.93e-16 1.01e-15 6.0e-15 3.1e+11 1.4e-13 2.99e-04
##
## ***** FALSE CONVERGENCE *****
##
## FUNCTION 1.737761e+03 RELDX 6.009e-15
## FUNC. EVALS 76 GRAD. EVALS 35
## PRELDF 1.013e-15 NPRELDF 2.991e-04
##
## I FINAL X(I) D(I) G(I)
##
## 1 7.350539e+00 1.000e+00 5.008e-01
## 2 1.446907e-01 1.000e+00 -4.113e+00
## 3 6.110465e-02 1.000e+00 -8.233e+00
## 4 4.304983e-03 1.000e+00 4.954e+00
## 5 5.939996e-13 1.000e+00 7.386e+00#Modelo GARCH(2,2)
coeftest(ModeloGarch22)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## a0 7.3505e+00 4.0098e+00 1.8332 0.06678 .
## a1 1.4469e-01 3.2662e-02 4.4299 9.426e-06 ***
## a2 6.1105e-02 1.1225e-01 0.5443 0.58620
## b1 4.3050e-03 7.4673e-01 0.0058 0.99540
## b2 5.9400e-13 2.3699e-01 0.0000 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Modelo GARCH(0,2)
coeftest(ModeloGarch02)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## a0 7.141701 0.209866 34.0299 < 2.2e-16 ***
## a1 0.154382 0.031623 4.8819 1.051e-06 ***
## a2 0.083880 0.026649 3.1476 0.001646 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo GARCH(1,1)
coeftest(ModeloGarch11)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## a0 8.2678e+00 9.2890e-01 8.9007 < 2.2e-16 ***
## a1 1.3960e-01 3.2440e-02 4.3033 1.683e-05 ***
## b1 1.0049e-12 1.0083e-01 0.0000 1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 18.3 Selección del Mejor Modelo
TablaDiagnosticoGarch <-
rbind.data.frame(
list('ModeloGarch11' ,
all(coeftest(ModeloGarch11)[,4] <=
0.05),AIC(ModeloGarch11)),
list('ModeloGarch02' ,
all(coeftest(ModeloGarch02)[,4] <=
0.05),AIC(ModeloGarch02)),
list('ModeloGarch22' ,
all(coeftest(ModeloGarch22)[,4] <=
0.05),AIC(ModeloGarch22))
)
names(TablaDiagnosticoGarch) <-
c('Modelo','AllCoef<0.05?','AIC')
TablaDiagnosticoGarch <- TablaDiagnosticoGarch[order(-
TablaDiagnosticoGarch$`AllCoef<0.05`,TablaDiagnosticoGarch$
AIC),]
head(TablaDiagnosticoGarch)| Modelo | AllCoef<0.05? | AIC | |
|---|---|---|---|
| 2 | ModeloGarch02 | TRUE | 5491.800 |
| 3 | ModeloGarch22 | FALSE | 5496.159 |
| 1 | ModeloGarch11 | FALSE | 5502.959 |
coeftest(ModeloGarch02)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## a0 7.141701 0.209866 34.0299 < 2.2e-16 ***
## a1 0.154382 0.031623 4.8819 1.051e-06 ***
## a2 0.083880 0.026649 3.1476 0.001646 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ModeloGarchElegido <- ModeloGarch02El modelo garch02 es el modelo que estimara la varianza condicional de la serie de los retornos.
8.4 Comprobación del modelo ajustado
par(mfrow=c(2,2))
plot.ts(residuals(ModeloGarchElegido),main = 'Residuos,Modelo en Varianza, Garch(0,2)')
qqnorm(residuals(ModeloGarchElegido))
qqline(residuals(ModeloGarchElegido))
acf(residuals(ModeloGarchElegido)^2,na.action = na.omit)
pacf(residuals(ModeloGarchElegido)^2,na.action = na.omit)
9 Presentación Modelo ARIMA-GARCH estimado
fit <- fitted.values(ModeloArimaElegido)
fitgarch <- fitted.values(ModeloGarchElegido)[,1]
low <- fit - (1.96 * fitgarch)
high <- fit + (1.96 * fitgarch)
plot(ret,
main = 'Google: Retornos VS Ajuste de Retornos con
Modelo ARIMA(2,1,1)-GRACH(0,2)',
type = 'l')
lines(low,col = 'purple')
lines(high,col = 'purple')
lines(fit,col = 'red') 
coeftest(ModeloArima211)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.1525878 0.0298604 5.1100 3.221e-07 ***
## ar2 0.1767687 0.0298539 5.9211 3.197e-09 ***
## ma1 -0.9999999 0.0026799 -373.1484 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 coeftest(ModeloGarch02)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## a0 7.141701 0.209866 34.0299 < 2.2e-16 ***
## a1 0.154382 0.031623 4.8819 1.051e-06 ***
## a2 0.083880 0.026649 3.1476 0.001646 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 predict(ModeloGarch02,n.ahead=5)## Time Series:
## Start = 2
## End = 1097
## Frequency = 1
## [,1] [,2]
## 2 NA NA
## 3 NA NA
## 4 2.717260 -2.717260
## 5 2.742022 -2.742022
## 6 2.716042 -2.716042
## 7 2.706146 -2.706146
## 8 2.803603 -2.803603
## 9 2.737954 -2.737954
## 10 3.493368 -3.493368
## 11 3.485848 -3.485848
## 12 2.973143 -2.973143
## 13 2.883784 -2.883784
## 14 2.792537 -2.792537
## 15 3.688857 -3.688857
## 16 3.438484 -3.438484
## 17 2.835423 -2.835423
## 18 2.743086 -2.743086
## 19 2.724192 -2.724192
## 20 2.724856 -2.724856
## 21 2.695248 -2.695248
## 22 2.839707 -2.839707
## 23 2.765913 -2.765913
## 24 2.674964 -2.674964
## 25 2.792614 -2.792614
## 26 2.846169 -2.846169
## 27 2.748830 -2.748830
## 28 2.681592 -2.681592
## 29 2.752539 -2.752539
## 30 2.716232 -2.716232
## 31 2.673781 -2.673781
## 32 2.782058 -2.782058
## 33 2.863498 -2.863498
## 34 3.065053 -3.065053
## 35 2.884418 -2.884418
## 36 2.724682 -2.724682
## 37 2.700869 -2.700869
## 38 3.153894 -3.153894
## 39 3.164254 -3.164254
## 40 3.039782 -3.039782
## 41 2.841226 -2.841226
## 42 2.708533 -2.708533
## 43 2.738758 -2.738758
## 44 3.020470 -3.020470
## 45 2.958788 -2.958788
## 46 2.736443 -2.736443
## 47 2.686393 -2.686393
## 48 2.684164 -2.684164
## 49 2.788468 -2.788468
## 50 2.794030 -2.794030
## 51 2.815727 -2.815727
## 52 2.859484 -2.859484
## 53 3.346748 -3.346748
## 54 3.028319 -3.028319
## 55 3.144604 -3.144604
## 56 3.343411 -3.343411
## 57 2.924229 -2.924229
## 58 2.764280 -2.764280
## 59 2.827755 -2.827755
## 60 2.768553 -2.768553
## 61 2.725663 -2.725663
## 62 2.695218 -2.695218
## 63 2.678695 -2.678695
## 64 2.712984 -2.712984
## 65 2.704128 -2.704128
## 66 3.202182 -3.202182
## 67 3.047893 -3.047893
## 68 2.811682 -2.811682
## 69 2.844474 -2.844474
## 70 2.787257 -2.787257
## 71 2.758856 -2.758856
## 72 2.715149 -2.715149
## 73 2.737100 -2.737100
## 74 2.822861 -2.822861
## 75 2.742071 -2.742071
## 76 2.744302 -2.744302
## 77 2.741097 -2.741097
## 78 2.691258 -2.691258
## 79 2.679634 -2.679634
## 80 2.797224 -2.797224
## 81 2.794485 -2.794485
## 82 2.720415 -2.720415
## 83 2.917023 -2.917023
## 84 2.822736 -2.822736
## 85 2.690289 -2.690289
## 86 2.679206 -2.679206
## 87 2.693569 -2.693569
## 88 2.684274 -2.684274
## 89 2.673118 -2.673118
## 90 2.682762 -2.682762
## 91 2.722076 -2.722076
## 92 2.756278 -2.756278
## 93 2.705419 -2.705419
## 94 2.700819 -2.700819
## 95 2.688004 -2.688004
## 96 2.710731 -2.710731
## 97 2.708560 -2.708560
## 98 2.685248 -2.685248
## 99 2.705744 -2.705744
## 100 2.804893 -2.804893
## 101 3.235702 -3.235702
## 102 2.966439 -2.966439
## 103 2.749009 -2.749009
## 104 2.712278 -2.712278
## 105 2.819725 -2.819725
## 106 2.887636 -2.887636
## 107 3.366505 -3.366505
## 108 3.058538 -3.058538
## 109 2.715795 -2.715795
## 110 2.687585 -2.687585
## 111 2.712619 -2.712619
## 112 2.973580 -2.973580
## 113 2.829431 -2.829431
## 114 2.773621 -2.773621
## 115 2.778320 -2.778320
## 116 2.723319 -2.723319
## 117 2.859005 -2.859005
## 118 2.939307 -2.939307
## 119 2.773726 -2.773726
## 120 2.704383 -2.704383
## 121 2.738777 -2.738777
## 122 3.361568 -3.361568
## 123 3.053236 -3.053236
## 124 2.978076 -2.978076
## 125 2.843102 -2.843102
## 126 2.708726 -2.708726
## 127 2.893982 -2.893982
## 128 2.787202 -2.787202
## 129 2.706136 -2.706136
## 130 2.821093 -2.821093
## 131 2.746372 -2.746372
## 132 3.424703 -3.424703
## 133 3.135743 -3.135743
## 134 2.730391 -2.730391
## 135 2.693963 -2.693963
## 136 3.052682 -3.052682
## 137 3.306739 -3.306739
## 138 3.098064 -3.098064
## 139 2.776032 -2.776032
## 140 2.696705 -2.696705
## 141 2.702322 -2.702322
## 142 3.073659 -3.073659
## 143 3.128936 -3.128936
## 144 2.841480 -2.841480
## 145 2.868260 -2.868260
## 146 2.778798 -2.778798
## 147 2.697876 -2.697876
## 148 2.685366 -2.685366
## 149 3.040823 -3.040823
## 150 2.881902 -2.881902
## 151 2.834597 -2.834597
## 152 2.760578 -2.760578
## 153 2.802881 -2.802881
## 154 2.745229 -2.745229
## 155 2.980530 -2.980530
## 156 3.298161 -3.298161
## 157 2.963036 -2.963036
## 158 2.712141 -2.712141
## 159 4.017315 -4.017315
## 160 3.462300 -3.462300
## 161 2.745936 -2.745936
## 162 2.905887 -2.905887
## 163 2.817126 -2.817126
## 164 2.711099 -2.711099
## 165 2.797085 -2.797085
## 166 2.735599 -2.735599
## 167 2.672734 -2.672734
## 168 2.678156 -2.678156
## 169 2.678000 -2.678000
## 170 2.674802 -2.674802
## 171 2.676734 -2.676734
## 172 2.903081 -2.903081
## 173 2.832220 -2.832220
## 174 3.018502 -3.018502
## 175 2.881126 -2.881126
## 176 2.745473 -2.745473
## 177 2.710471 -2.710471
## 178 2.678127 -2.678127
## 179 2.680389 -2.680389
## 180 2.707858 -2.707858
## 181 2.715860 -2.715860
## 182 2.686904 -2.686904
## 183 2.684855 -2.684855
## 184 2.682677 -2.682677
## 185 2.723600 -2.723600
## 186 2.750184 -2.750184
## 187 2.759778 -2.759778
## 188 2.736380 -2.736380
## 189 2.714933 -2.714933
## 190 2.695034 -2.695034
## 191 2.730824 -2.730824
## 192 2.702613 -2.702613
## 193 2.727703 -2.727703
## 194 2.717180 -2.717180
## 195 2.764436 -2.764436
## 196 2.737365 -2.737365
## 197 2.687645 -2.687645
## 198 2.686379 -2.686379
## 199 2.692234 -2.692234
## 200 2.680016 -2.680016
## 201 2.678898 -2.678898
## 202 2.737718 -2.737718
## 203 2.771629 -2.771629
## 204 2.751416 -2.751416
## 205 2.724508 -2.724508
## 206 2.704941 -2.704941
## 207 2.689188 -2.689188
## 208 2.679299 -2.679299
## 209 2.769321 -2.769321
## 210 2.728692 -2.728692
## 211 3.807211 -3.807211
## 212 3.364003 -3.364003
## 213 3.456418 -3.456418
## 214 3.136852 -3.136852
## 215 2.692150 -2.692150
## 216 2.682265 -2.682265
## 217 2.683379 -2.683379
## 218 2.678342 -2.678342
## 219 2.673980 -2.673980
## 220 2.672659 -2.672659
## 221 2.672591 -2.672591
## 222 2.676656 -2.676656
## 223 2.682149 -2.682149
## 224 2.693234 -2.693234
## 225 2.683655 -2.683655
## 226 2.682040 -2.682040
## 227 3.386987 -3.386987
## 228 3.100602 -3.100602
## 229 3.421767 -3.421767
## 230 3.146729 -3.146729
## 231 2.706378 -2.706378
## 232 2.680727 -2.680727
## 233 3.123700 -3.123700
## 234 2.932760 -2.932760
## 235 2.717065 -2.717065
## 236 2.729826 -2.729826
## 237 3.038381 -3.038381
## 238 2.871664 -2.871664
## 239 2.836531 -2.836531
## 240 2.761890 -2.761890
## 241 2.679830 -2.679830
## 242 2.690072 -2.690072
## 243 2.686548 -2.686548
## 244 2.682753 -2.682753
## 245 2.730319 -2.730319
## 246 2.702183 -2.702183
## 247 2.798071 -2.798071
## 248 2.777429 -2.777429
## 249 2.742228 -2.742228
## 250 2.700583 -2.700583
## 251 2.673388 -2.673388
## 252 2.673052 -2.673052
## 253 2.673335 -2.673335
## 254 2.672981 -2.672981
## 255 2.859864 -2.859864
## 256 3.024180 -3.024180
## 257 3.238355 -3.238355
## 258 3.045604 -3.045604
## 259 3.080309 -3.080309
## 260 3.514108 -3.514108
## 261 3.137629 -3.137629
## 262 2.841005 -2.841005
## 263 2.741295 -2.741295
## 264 3.713707 -3.713707
## 265 3.282324 -3.282324
## 266 2.677045 -2.677045
## 267 2.697168 -2.697168
## 268 2.759950 -2.759950
## 269 3.607578 -3.607578
## 270 3.253493 -3.253493
## 271 2.877584 -2.877584
## 272 2.885889 -2.885889
## 273 2.924810 -2.924810
## 274 3.109815 -3.109815
## 275 3.046108 -3.046108
## 276 2.918308 -2.918308
## 277 2.822253 -2.822253
## 278 3.009201 -3.009201
## 279 3.167474 -3.167474
## 280 3.128510 -3.128510
## 281 2.828695 -2.828695
## 282 2.703827 -2.703827
## 283 2.690896 -2.690896
## 284 2.684140 -2.684140
## 285 3.353574 -3.353574
## 286 3.574564 -3.574564
## 287 3.246119 -3.246119
## 288 2.869473 -2.869473
## 289 2.702530 -2.702530
## 290 2.688639 -2.688639
## 291 2.787318 -2.787318
## 292 2.763752 -2.763752
## 293 2.711181 -2.711181
## 294 2.874805 -2.874805
## 295 3.060388 -3.060388
## 296 5.488408 -5.488408
## 297 4.665003 -4.665003
## 298 2.976653 -2.976653
## 299 2.704307 -2.704307
## 300 2.681646 -2.681646
## 301 2.847138 -2.847138
## 302 2.806196 -2.806196
## 303 3.205735 -3.205735
## 304 2.963193 -2.963193
## 305 2.717735 -2.717735
## 306 2.718800 -2.718800
## 307 3.338165 -3.338165
## 308 3.200654 -3.200654
## 309 3.046823 -3.046823
## 310 2.839019 -2.839019
## 311 3.316431 -3.316431
## 312 3.038582 -3.038582
## 313 2.804477 -2.804477
## 314 2.744602 -2.744602
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