Following some standard textbooks on ARMA(1,1)-GARCH(1,1) (e.g. Ruey Tsay's Analysis of Financial Time Series), I try to write an R program to estimate the key parameters of an ARMA(1,1)-GARCH(1,1) model for Intel's stock returns. For some random reason, I cannot decipher what is wrong with my R program. The R package fGarch already gives me the answer, but my customized function does not seem to produce the same result.
I would like to build an R program that helps estimate the baseline ARMA(1,1)-GARCH(1,1) model. Then I would like to adapt this baseline script to fit different GARCH variants (e.g. EGARCH, NGARCH, and TGARCH). It would be much appreciated if you could provide some guidance in this case. The code below is the R script for estimating the 6 parameters of an ARMA(1,1)-GARCH(1,1) model for Intel's stock returns. At any rate, I would be glad to know your thoughts and insights. If you have a similar example, please feel free to share your extant code in R. Many thanks in advance.
Emily
# This R script offers a suite of functions for estimating the volatility dynamics based on the standard ARMA(1,1)-GARCH(1,1) model and its variants.
# The baseline ARMA(1,1) model characterizes the dynamic evolution of the return generating process.
# The baseline GARCH(1,1) model depicts the the return volatility dynamics over time.
# We can extend the GARCH(1,1) volatility model to a variety of alternative specifications to capture the potential asymmetry for a better comparison:
# GARCH(1,1), EGARCH(1,1), NGARCH(1,1), and TGARCH(1,1).
options(scipen=10)
intel= read.csv(file="intel.csv")
summary(intel)
raw_data= as.matrix(intel$logret)
library(fGarch)
garchFit(~arma(1,1)+garch(1,1), data=raw_data, trace=FALSE)
negative_log_likelihood_arma11_garch11=
function(theta, data)
{mean =theta[1]
delta=theta[2]
gamma=theta[3]
omega=theta[4]
alpha=theta[5]
beta= theta[6]
r= ts(data)
n= length(r)
u= vector(length=n)
u= ts(u)
u[1]= r[1]- mean
for (t in 2:n)
{u[t]= r[t]- mean- delta*r[t-1]- gamma*u[t-1]}
h= vector(length=n)
h= ts(h)
h[1]= omega/(1-alpha-beta)
for (t in 2:n)
{h[t]= omega+ alpha*(u[t-1]^2)+ beta*h[t-1]}
#return(-sum(dnorm(u[2:n], mean=mean, sd=sqrt(h[2:n]), log=TRUE)))
pi=3.141592653589793238462643383279502884197169399375105820974944592
return(-sum(-0.5*log(2*pi) -0.5*log(h[2:n]) -0.5*(u[2:n]^2)/h[2:n]))
}
#theta0=c(0, +0.78, -0.79, +0.0000018, +0.06, +0.93, 0.01)
theta0=rep(0.01,6)
negative_log_likelihood_arma11_garch11(theta=theta0, data=raw_data)
alpha= proc.time()
maximum_likelihood_fit_arma11_garch11=
nlm(negative_log_likelihood_arma11_garch11,
p=theta0,
data=raw_data,
hessian=TRUE,
iterlim=500)
#optim(theta0,
# negative_log_likelihood_arma11_garch11,
# data=raw_data,
# method="L-BFGS-B",
# upper=c(+0.999999999999,+0.999999999999,+0.999999999999,0.999999999999,0.999999999999,0.999999999999),
# lower=c(-0.999999999999,-0.999999999999,-0.999999999999,0.000000000001,0.000000000001,0.000000000001),
# hessian=TRUE)
# We record the end time and calculate the total runtime for the above work.
omega= proc.time()
runtime= omega-alpha
zhours = floor(runtime/60/60)
zminutes=floor(runtime/60- zhours*60)
zseconds=floor(runtime- zhours*60*60- zminutes*60)
print(paste("It takes ",zhours,"hour(s)", zminutes," minute(s) ","and ", zseconds,"second(s) to finish running this R program",sep=""))
maximum_likelihood_fit_arma11_garch11
sqrt(diag(solve(maximum_likelihood_fit_arma11_garch11$hessian)))
