r - Maximum likelihood estimation for ARMA(1,1)-GARCH(1,1) -

following standard textbooks on arma(1,1)-garch(1,1) (e.g. ruey tsay's analysis of financial time series), try write r program estimate key parameters of arma(1,1)-garch(1,1) model intel's stock returns. random reason, cannot decipher wrong r program. r package fgarch gives me answer, customized function not seem produce same result.

i build r program helps estimate baseline arma(1,1)-garch(1,1) model. adapt baseline script fit different garch variants (e.g. egarch, ngarch, , tgarch). appreciated if provide guidance in case. code below r script estimating 6 parameters of arma(1,1)-garch(1,1) model intel's stock returns. @ rate, glad know thoughts , insights. if have similar example, please feel free share extant code in r. many in advance.

emily

# r script offers suite of functions estimating  volatility dynamics based on standard arma(1,1)-garch(1,1) model , variants. # baseline arma(1,1) model characterizes dynamic evolution of return generating process.  # baseline garch(1,1) model depicts the return volatility dynamics on time. # can extend garch(1,1) volatility model variety of alternative specifications capture potential asymmetry better comparison: # garch(1,1), egarch(1,1),  ngarch(1,1), , tgarch(1,1).  options(scipen=10)  intel= read.csv(file="intel.csv") summary(intel)  raw_data= as.matrix(intel$logret)  library(fgarch) garchfit(~arma(1,1)+garch(1,1), data=raw_data, trace=false)   negative_log_likelihood_arma11_garch11= function(theta, data) {mean =theta[1]  delta=theta[2]  gamma=theta[3]  omega=theta[4]  alpha=theta[5]  beta= theta[6]   r= ts(data)  n= length(r)   u= vector(length=n)  u= ts(u)  u[1]= r[1]- mean   (t in 2:n)  {u[t]= r[t]- mean- delta*r[t-1]- gamma*u[t-1]}   h= vector(length=n)  h= ts(h)  h[1]= omega/(1-alpha-beta)   (t in 2:n)  {h[t]= omega+ alpha*(u[t-1]^2)+ beta*h[t-1]}   #return(-sum(dnorm(u[2:n], mean=mean, sd=sqrt(h[2:n]), log=true)))  pi=3.141592653589793238462643383279502884197169399375105820974944592  return(-sum(-0.5*log(2*pi) -0.5*log(h[2:n]) -0.5*(u[2:n]^2)/h[2:n])) }   #theta0=c(0, +0.78, -0.79, +0.0000018, +0.06, +0.93, 0.01) theta0=rep(0.01,6) negative_log_likelihood_arma11_garch11(theta=theta0, data=raw_data)   alpha= proc.time() maximum_likelihood_fit_arma11_garch11= nlm(negative_log_likelihood_arma11_garch11,     p=theta0,     data=raw_data,     hessian=true,     iterlim=500) #optim(theta0,  #      negative_log_likelihood_arma11_garch11, #      data=raw_data, #      method="l-bfgs-b", #      upper=c(+0.999999999999,+0.999999999999,+0.999999999999,0.999999999999,0.999999999999,0.999999999999), #      lower=c(-0.999999999999,-0.999999999999,-0.999999999999,0.000000000001,0.000000000001,0.000000000001), #      hessian=true)  # record end time , calculate total runtime above work. omega= proc.time() runtime= omega-alpha zhours = floor(runtime/60/60) zminutes=floor(runtime/60- zhours*60) zseconds=floor(runtime- zhours*60*60- zminutes*60) print(paste("it takes ",zhours,"hour(s)", zminutes," minute(s) ","and ", zseconds,"second(s) finish running r program",sep=""))   maximum_likelihood_fit_arma11_garch11  sqrt(diag(solve(maximum_likelihood_fit_arma11_garch11$hessian)))