PARCIAL 2- ECONOMETRIA 2
Laura Zabala Solis -20210833
2024-11-13
Cargar los Paquetes Necesarios:
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## intersect, setdiff, setequal, unionDescargar Datos del Tipo de Cambio DOP/USD:
getSymbols("USDDOP=X", from="2015-01-01")## [1] "USDDOP=X"USD_DOP <-get("USDDOP=X")
help("quantmod")## starting httpd help server ... doneView(USD_DOP)Graficar los Datos del Tipo de Cambio:
plot(USD_DOP$`USDDOP=X.Adjusted`)
Calculo de Retornos Logarítmicos
USD_DOP_Return <- CalculateReturns(USD_DOP$`USDDOP=X.Adjusted`, method = "log")Calculo de la Volatilidad Anualizada
sqrt(252)*sd(USD_DOP_Return, na.rm = T)## [1] 0.147544El resultado de 0.1475717 significa que, la tasa de cambio podría variar hasta un 14.76% hacia arriba o hacia abajo durante un año. Es una forma de medir de cmo seran las fluctuaciones o cambio que pueden haber en el valor del dólar en comparación con el peso dominicano a lo largo de un año.
Calculo las Ventanas de Volatilidad
chart.RollingPerformance(R=USD_DOP_Return, width = 22, FUN = "sd.annualized", scale=252, main = "Volitilidad Rolling Anualizada del USD/DOP")
Este grafico muestra como es la volatilidad del Dolar/Peso, mostrando aquellos cambios mas relevante entre el 2018 y 2019, donde se muestran icos altos por ambios muy grandes, esto pudo ser por eventos economicos o politicos, ya sea locales, en la Republica Dominicana o por eventos externos. Despues del 2020 se observa una disminucion en los niveles de volatilidad, lo que significa se fue estabilizando el tipo de cambio en esos periodos.
Modelo GARCH()
anyNA(USD_DOP_Return)## [1] TRUEUSD_DOP_Return <-na.omit(USD_DOP_Return)
library(forcats)
library(forecast)## Warning: package 'forecast' was built under R version 4.3.3library(rugarch)
library(stargazer)##
## Please cite as:## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.3. https://CRAN.R-project.org/package=stargazerauto.arima(USD_DOP_Return)## Series: USD_DOP_Return
## ARIMA(1,0,1) with non-zero mean
##
## Coefficients:
## ar1 ma1 mean
## -0.0005 -0.7153 1e-04
## s.e. 0.0265 0.0178 0e+00
##
## sigma^2 = 5.716e-05: log likelihood = 8929.34
## AIC=-17850.67 AICc=-17850.66 BIC=-17827.26garchspec<-ugarchspec(mean.model = list(arma0rder=c(1,1)),
variance.model = list(model="sGARCH"),
distribution.model = "sstd")## Warning: unidentified option(s) in mean.model:
## arma0rdergarchfit<- ugarchfit(data = USD_DOP_Return,spec = garchspec)
garchforecast <- ugarchforecast(fitORspec = garchfit, n.ahead = 5)
#Coeficientes:
garchcoef<-coef(garchfit)
print(garchcoef)## mu ar1 ma1 omega alpha1
## -3.627148e-05 -2.954752e-02 -6.101151e-01 3.405560e-06 4.347448e-01
## beta1 skew shape
## 5.642551e-01 7.411115e-01 3.245674e+00#Varianza:
garchuncvar<-uncvariance(garchfit)
garchuncvar## [1] 0.003405116Ajustar el Modelo GARCH
Especificar y Ajustar un Modelo GJR-GARCH
#Paquete a Utilizar:
library(rugarch)
install.packages("rugarch")## Warning: package 'rugarch' is in use and will not be installedlibrary(rugarch)
#media predicha:
garchmean<-fitted(garchfit)
#volatilidad:
garchvol<-sigma(garchfit)
#Ajuste del MOdelo:
gjr_garch_spec <- ugarchspec(
mean.model = list(armaOrder = c(1, 1)),
variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)),
distribution.model = "sstd"
)
# Ajustar el modelo GJR-GARCH a los datos de retorno:
gjr_garch_fit <- ugarchfit(spec = gjr_garch_spec, data = USD_DOP_Return)
# la media predicha:
garchmean <- fitted(gjr_garch_fit)
# volatilidad estimada:
gjrgarchvol <- sigma(gjr_garch_fit)
# coeficientes del modelo ajustado:
gjrgarchcoef <- coef(gjr_garch_fit)
# Mostrar los coeficientes:
print(gjrgarchcoef)## mu ar1 ma1 omega alpha1
## -5.239831e-05 -2.155114e-02 -5.942694e-01 3.725494e-06 3.941301e-01
## beta1 gamma1 skew shape
## 5.454575e-01 1.397228e-01 7.411897e-01 3.177558e+00Comparacion de los Modelos Garch y GJR-Garch.
print(garchfit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(1,0,1)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000036 0.000030 -1.1909 0.233679
## ar1 -0.029548 0.023065 -1.2811 0.200174
## ma1 -0.610115 0.019637 -31.0694 0.000000
## omega 0.000003 0.000001 2.7168 0.006591
## alpha1 0.434745 0.033990 12.7904 0.000000
## beta1 0.564255 0.030287 18.6302 0.000000
## skew 0.741112 0.016228 45.6685 0.000000
## shape 3.245674 0.112764 28.7830 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000036 0.000041 -0.88226 0.377636
## ar1 -0.029548 0.025657 -1.15164 0.249470
## ma1 -0.610115 0.033547 -18.18678 0.000000
## omega 0.000003 0.000006 0.52850 0.597156
## alpha1 0.434745 0.082411 5.27532 0.000000
## beta1 0.564255 0.216961 2.60072 0.009303
## skew 0.741112 0.033123 22.37453 0.000000
## shape 3.245674 0.169834 19.11081 0.000000
##
## LogLikelihood : 9756.336
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.5686
## Bayes -7.5504
## Shibata -7.5686
## Hannan-Quinn -7.5620
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 4.669 3.072e-02
## Lag[2*(p+q)+(p+q)-1][5] 12.294 0.000e+00
## Lag[4*(p+q)+(p+q)-1][9] 15.964 1.196e-05
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.598 0.2062
## Lag[2*(p+q)+(p+q)-1][5] 3.380 0.3420
## Lag[4*(p+q)+(p+q)-1][9] 5.553 0.3528
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.8811 0.500 2.000 0.3479
## ARCH Lag[5] 1.2766 1.440 1.667 0.6530
## ARCH Lag[7] 2.7236 2.315 1.543 0.5672
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 62.2203
## Individual Statistics:
## mu 0.6056
## ar1 0.3235
## ma1 1.2601
## omega 0.3232
## alpha1 7.1218
## beta1 1.4279
## skew 5.8062
## shape 2.9252
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.89 2.11 2.59
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.493 0.1356455
## Negative Sign Bias 1.557 0.1196349
## Positive Sign Bias 3.572 0.0003602 ***
## Joint Effect 16.294 0.0009868 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 72.62 3.359e-08
## 2 30 94.72 6.716e-09
## 3 40 116.86 1.060e-09
## 4 50 127.14 7.277e-09
##
##
## Elapsed time : 2.230694print(gjr_garch_fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(1,0,1)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000052 0.000033 -1.59481 0.110755
## ar1 -0.021551 0.024355 -0.88488 0.376223
## ma1 -0.594269 0.021613 -27.49599 0.000000
## omega 0.000004 0.000001 4.05432 0.000050
## alpha1 0.394130 0.041195 9.56751 0.000000
## beta1 0.545457 0.020534 26.56395 0.000000
## gamma1 0.139723 0.061201 2.28302 0.022429
## skew 0.741190 0.016343 45.35195 0.000000
## shape 3.177558 0.110690 28.70686 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000052 0.000045 -1.16769 0.242931
## ar1 -0.021551 0.027638 -0.77976 0.435533
## ma1 -0.594269 0.042874 -13.86077 0.000000
## omega 0.000004 0.000003 1.18752 0.235024
## alpha1 0.394130 0.039479 9.98323 0.000000
## beta1 0.545457 0.125582 4.34343 0.000014
## gamma1 0.139723 0.182068 0.76742 0.442831
## skew 0.741190 0.028899 25.64747 0.000000
## shape 3.177558 0.143154 22.19684 0.000000
##
## LogLikelihood : 9758.21
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.5693
## Bayes -7.5488
## Shibata -7.5693
## Hannan-Quinn -7.5618
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 6.424 1.126e-02
## Lag[2*(p+q)+(p+q)-1][5] 14.743 0.000e+00
## Lag[4*(p+q)+(p+q)-1][9] 18.596 4.515e-07
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.807 0.1789
## Lag[2*(p+q)+(p+q)-1][5] 3.745 0.2876
## Lag[4*(p+q)+(p+q)-1][9] 6.190 0.2769
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.9716 0.500 2.000 0.3243
## ARCH Lag[5] 1.4013 1.440 1.667 0.6186
## ARCH Lag[7] 3.1555 2.315 1.543 0.4847
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 68.6569
## Individual Statistics:
## mu 0.6713
## ar1 0.3514
## ma1 1.2490
## omega 0.3165
## alpha1 7.3795
## beta1 1.3465
## gamma1 5.3106
## skew 6.0345
## shape 2.7759
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.1 2.32 2.82
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.530 0.1262178
## Negative Sign Bias 1.703 0.0887750 *
## Positive Sign Bias 3.539 0.0004093 ***
## Joint Effect 16.955 0.0007221 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 84.53 3.045e-10
## 2 30 98.82 1.509e-09
## 3 40 111.92 5.740e-09
## 4 50 143.14 3.736e-11
##
##
## Elapsed time : 4.024892Diagnóstico de los Residuos:
RESIDUOS_Garch <-residuals(garchfit)
plot(RESIDUOS_Garch, main= "Residuos Garch Estandarizados", col= "royalblue" )
RESIDUOS_GJRGARCH<- residuals(gjr_garch_fit)
plot(RESIDUOS_GJRGARCH, main= "Residuos Estandarizados GJR-Garch", col= "peru")
Analizar la Volatilidad Condicional
library(quantmod)
VOLATILIDAD_USD_DOP <- plot(abs(gjrgarchvol), col = "darkblue", main = "Volatilidad Condicional: GARCH vs GJR-GARCH",
ylab = "Volatilidad Condicional", xlab = "Tiempo")
VOLATILIDAD_USD_DOP <- addSeries(garchvol, col = "lightblue", on = 1)
#Muestra del Grafico Final
show(VOLATILIDAD_USD_DOP)
Evaluar la Volatilidad y su Impacto en el Ahorro
Segun los Datos obtenidos, se puede observar que la volatilidad del Dolar/Peso es bastante alta, lo que significa que el valor del peso, frente al dólar puede fluctuar mucho mas. Esto significa que, si se ahorra en pesos, los ahorros podrían perder valor rápidamente debido a la volatilidad en el tipo de cambio. Por otro lado, el dólar tiende a ser más estable y, por lo tanto, ahorrar en dólares podría ser una opción más segura para mantener el valor de los ahorros a largo plazo.
Consideraciones Económicas Adicionales
La inflación es un facto importante, ya que si el país experimenta una alta inflación, el valor de los ahorros en pesos se depresia rápidamente, lo que hace que ahorrar en dólares la mejor opcion, debido a la menor inflación de esta moneda. Además, las tasas de interés en pesos pueden influir positivamente en el rendimiento de los ahorros, especialmente si son altas. Ademas, este beneficio puede verse compensado si la inflación también es elevada o si la volatilidad del peso afecta negativamente el valor real de los ahorros, haciendo que el riesgo de fluctuaciones en el tipo de cambio sea un factor determinante.
Conclusión Final
Dado que la volatilidad en el peso es alta, lo más seguro sería ahorrar en dólares, ya que esta moneda es más estable y puede ayudar a proteger mejor el valor de los ahorros frente a las fluctuaciones del tipo de cambio.