[R-SIG-Finance] [R] Maximum likelihood estimation of ARMA(1, 1)-GARCH(1, 1)

[R. Michael Weylandt]

Forwarding to r-sig-finance where you might get a better response.

MW

On Mon, Apr 8, 2013 at 5:30 AM, Andy Yeh <rochefort2010 at gmail.com> wrote:
> Hello
>
> 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)))
>
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