Maximum Likelihood estimation NGARCH Model in R - r

Question

Calc<-function(th,t){
th[1]->mean
th[2]->beta.0
th[3]->beta.1
th[4]->beta.2
th[5]->sigma.0
th[6]->lambda
returns<-returnzzzz$ReturnontheSP500Index
r<-0.000137
n<-length(returns)
z<-rnorm(n,0,1)#sigma is variance
sigma.sqs<-vector(length=n)
sigma.sqs[1]<-sigma.0**2
for(i in c(1:(n))){
returns[i+1]<-( r+lambda*sqrt(beta.0+beta.1*sigma.sqs[i]+beta.2*sigma.sqs[i]*z**2)
-0.5*(beta.0+beta.1*sigma.sqs[i]+beta.2*sigma.sqs[i]*z**2)+sqrt(beta.0+beta.1*sigma.sqs[i]+beta.2*sigma.sqs[i]*z**2)*z
)
}
return(list(et=returns, ht=sigma.sqs))
}
GarchLogL<-function(th,t)
{
res<-Calc(th,t)
sigma.sqs<-res$ht
returns<-res$et
return (-sum(dnorm(returns[-1],mean=th[1],sd=sqrt(sigma.sqs[-1]),log=TRUE)))
}
GarchLogLSimpl<-function(th,y){GarchLogL(c(0,th),y)}
fit2<-nlm(GarchLogLSimpl,
p=rep(1,5),
hessian=TRUE,
data<-returnzzzz,
iterlim=500)
sqrt(diag(solve(fit2$hessian)))
Hi this is the first time for me here, i hope i do everything right. In this code i want to implement a maximum likelihood function of the N-GARCH, i get this error out of R: There were 50 or more warnings (use warnings() to see the first 50) and this one Error in solve.default(fit2$hessian) :
Lapack routine dgesv: system is exactly singular: U[1,1] = 0.
Unfortunately i am not a really good programmer and i just changed a GARCH model code for my needs. My return data is
# [,1]
#1996-01-02 0.007793
#1996-01-03 0.000950
#1996-01-04 -0.005826
#1996-01-05 -0.001587
#1996-01-08 0.002821
#1996-01-09 -0.014568
like this, as an xts. I hope i provided enough information, if not pls just comment.
I really appreciate your help!!
I got a new code that might be able to solve it, but I get another error in this one:
Ngarch<-function(rtn){
mu=mean(rtn)
par=c(mu,0.01,0.8,0.01,0.7) #Startwerte
low=c(-10,0,0,0,0)
upp=c(10,1,1,0.4,2)
mm=optim(par,glkn,method="Nelder-Mead",hessian=T)
#mm=optim(par,glkn,method="L-BFGS-B",hessian=T,lower=low,upper=upp)
par=mm$par
H=mm$hessian
Hi = solve(H)
cat(" ","\n")
cat("Estimation results of NGARCH(1,1) model:","\n")
cat("estimates: ",par,"\n")
se=sqrt(diag(Hi))
cat("std.errors: ",se,"\n")
tra=par/se
cat("t-ratio: ",tra,"\n")
# compute the volatility series and residuals
ht=var(rtn)
T=length(rtn)
if(T > 40)ht=var(rtn[1:40])
at=rtn-par[1]
for (i in 2:T){
sig2t=par[2]+par[3]*ht[i-1]+par[4]*(at[i-1]-par[5]*sqrt(ht[i-1]))^2
ht=c(ht,sig2t)
}
sigma.t=sqrt(ht)
Ngarch <- list(residuals=at,volatility=sigma.t)
}
glkn <- function(par){
rtn=read.table("tmp.txt")[,1]
glkn=0
ht=var(rtn)
T=length(rtn)
if(T > 40)ht=var(rtn[1:40])
at=rtn[1]-par[1]
for (i in 2:T){
ept=rtn[i]-par[1]
at=c(at,ept)
sig2t=par[2]+par[3]*ht[i-1]+par[4]*ht[i-1]*(at[i-1]/sqrt(ht[i-1])-par[5])^2
ht=c(ht,sig2t)
glkn=glkn + 0.5*(log(sig2t) + ept^2/sig2t)
}
glkn
}
The error I get is Error in optim(par, glkn, method = "Nelder-Mead", hessian = T) :
non-finite finite-difference value [2].
An again these warnings, how can I get rid of them?
Thanks for your help!