Testing standardized residuals from GARCH(GED) model - AD test in R?

General
,
1

Hi everyone,

Background:
I estimated ARMA-GARCH(GED) model on single stock returns using EViews (not rugarch). I have:

  • Standardized residuals from EViews GARCH(GED) model
  • Model coefficients from EViews
  • EViews doesn't have Anderson-Darling test

Question:
How to run Anderson-Darling test in R on my EViews GARCH(GED) standardized residuals?

My data:

  • xlsx file with standardized residuals (resid01) exported from EViews
  • GED shape parameter from EViews output

What I need:

  1. R code to read EViews residuals + run AD test vs GED distribution
  2. Correct interpretation for GED standardized residuals

I already tried this AD test code for my EViews GARCH(GED) standardized residuals:

install.packages("readxl")
install.packages("fGarch")
install.packages("goftest")

library(readxl)
library(fGarch)
library(goftest)

data <- read_excel("C:/Users/myusername/Skripsi/1. data/resid01.xlsx")
z <- data$resid01
z <- na.omit(z)
mean(z)
sd(z)

Box.test(z, lag = 20, type = "Ljung-Box")

Box.test(z^2, lag = 20, type = "Ljung-Box")


### ==============================
### ANDERSON-DARLING TEST FOR GED
### ==============================

nu <-  1.127493  # shape

ad.test(z,
        null = pged,
        mean = 0,
        sd = 1,
        nu = nu)

### ==============================
### QQ-PLOT GED
### ==============================

n <- length(z)
p <- ppoints(n)
q_theoretical <- qged(p, mean = 0, sd = 1, nu = nu)
z_sorted <- sort(z)

# plot
plot(q_theoretical, z_sorted,
     main = "QQ-Plot Standardized Residual vs GED",
     xlab = "Theoretical GED Quantiles",
     ylab = "Sample Quantiles")

abline(0, 1, col = "red", lwd = 2)

qqplot_ged
qqplot_ged862×636 8.72 KB

RESULTS from this code: Residuals FOLLOW GED distribution (p > 0.05 + Perfect fit in middle, BUT tails deviate)

My questions:

  1. Is my ad.test() code correct for EViews GARCH(GED) residuals?
  2. Why different AD test codes give opposite results? Should I trust my code (accepts GED) or the other codes (reject GED)?
  3. Why QQ-plot tails deviate despite AD test accepting GED?
  4. What do tail deviations mean for GARCH(GED) model validity?
  5. Should I trust AD test or worry about QQ-plot tails?

Please help for my thesis, thank you