SEMANA 2

##Modelo de volativilidad

options(scipen=999)
pkges<-c("pdfetch","tseries","tidyverse","forecast")
#install.packages(pkges)
lapply(pkges,"library",character.only=T)
## [[1]]
## [1] "pdfetch"   "stats"     "graphics"  "grDevices" "utils"     "datasets" 
## [7] "methods"   "base"     
## 
## [[2]]
## [1] "tseries"   "pdfetch"   "stats"     "graphics"  "grDevices" "utils"    
## [7] "datasets"  "methods"   "base"     
## 
## [[3]]
##  [1] "forcats"   "stringr"   "dplyr"     "purrr"     "readr"     "tidyr"    
##  [7] "tibble"    "ggplot2"   "tidyverse" "tseries"   "pdfetch"   "stats"    
## [13] "graphics"  "grDevices" "utils"     "datasets"  "methods"   "base"     
## 
## [[4]]
##  [1] "forecast"  "forcats"   "stringr"   "dplyr"     "purrr"     "readr"    
##  [7] "tidyr"     "tibble"    "ggplot2"   "tidyverse" "tseries"   "pdfetch"  
## [13] "stats"     "graphics"  "grDevices" "utils"     "datasets"  "methods"  
## [19] "base"
RUSELL200 <- pdfetch_YAHOO("^RUT",interval = '1d')  #DATOS DE RUSELL200
tsRUSELL200 <- RUSELL200[,4]

##Calculamos retornos

R1 <- diff(log(tsRUSELL200))
R1 <- na.omit(R1)

Modelo Autorregresivo con Heterocedasticidad Condicional (ARCH)

plot.ts(R1)

hist(R1, main="", breaks=20, freq=FALSE, col="grey")

acf(R1)

ts.arch <- garch(R1,c(0,1))
## 
##  ***** ESTIMATION WITH ANALYTICAL GRADIENT ***** 
## 
## 
##      I     INITIAL X(I)        D(I)
## 
##      1     2.588920e-04     1.000e+00
##      2     5.000000e-02     1.000e+00
## 
##     IT   NF      F         RELDF    PRELDF    RELDX   STPPAR   D*STEP   NPRELDF
##      0    1 -1.228e+04
##      1    7 -1.230e+04  1.25e-03  1.79e-03  2.7e-04  3.0e+10  2.7e-05  2.70e+07
##      2    8 -1.230e+04  1.10e-04  1.66e-04  2.3e-04  2.0e+00  2.7e-05  1.58e+02
##      3    9 -1.230e+04  2.10e-05  2.28e-05  2.7e-04  2.0e+00  2.7e-05  1.55e+02
##      4   16 -1.239e+04  7.55e-03  1.26e-02  4.4e-01  2.0e+00  8.0e-02  1.54e+02
##      5   17 -1.243e+04  2.86e-03  2.39e-03  1.7e-01  0.0e+00  5.4e-02  2.39e-03
##      6   19 -1.246e+04  2.45e-03  1.68e-03  1.8e-01  0.0e+00  7.9e-02  1.68e-03
##      7   20 -1.247e+04  1.11e-03  8.78e-04  1.3e-01  1.2e-01  7.9e-02  8.86e-04
##      8   21 -1.248e+04  5.39e-04  3.99e-04  9.4e-02  0.0e+00  7.1e-02  3.99e-04
##      9   22 -1.248e+04  1.29e-04  1.03e-04  5.3e-02  0.0e+00  4.6e-02  1.03e-04
##     10   23 -1.248e+04  1.41e-05  1.23e-05  2.1e-02  0.0e+00  1.9e-02  1.23e-05
##     11   24 -1.248e+04  4.02e-07  3.82e-07  3.8e-03  0.0e+00  3.7e-03  3.82e-07
##     12   25 -1.248e+04  1.31e-09  1.30e-09  2.3e-04  0.0e+00  2.2e-04  1.30e-09
##     13   26 -1.248e+04  1.27e-13  1.26e-13  2.2e-06  0.0e+00  2.2e-06  1.26e-13
## 
##  ***** RELATIVE FUNCTION CONVERGENCE *****
## 
##  FUNCTION    -1.247967e+04   RELDX        2.232e-06
##  FUNC. EVALS      26         GRAD. EVALS      14
##  PRELDF       1.256e-13      NPRELDF      1.256e-13
## 
##      I      FINAL X(I)        D(I)          G(I)
## 
##      1    1.518198e-04     1.000e+00     1.851e-02
##      2    4.836897e-01     1.000e+00    -6.729e-08
summary(ts.arch)
## 
## Call:
## garch(x = R1, order = c(0, 1))
## 
## Model:
## GARCH(0,1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -9.10884 -0.45883  0.06567  0.55330  6.12675 
## 
## Coefficient(s):
##       Estimate  Std. Error  t value            Pr(>|t|)    
## a0 0.000151820 0.000002975    51.03 <0.0000000000000002 ***
## a1 0.483689728 0.024735224    19.55 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Diagnostic Tests:
##  Jarque Bera Test
## 
## data:  Residuals
## X-squared = 4741.7, df = 2, p-value < 0.00000000000000022
## 
## 
##  Box-Ljung test
## 
## data:  Squared.Residuals
## X-squared = 6.072, df = 1, p-value = 0.01373