Hey,
i am trying to do the MLE for Garch and have a problem with the optim
function.
Initally i tried optim with Method=BFGS. Reading trhough the forum i found
out
i would neet bounds. So i went on with Method=L-BFGS-B.
But now my parameters equal the lower bounds.
> out <- optim(par=initial, fn=LogLik.GARCH,X=X, P=1, Q=1, method >
"L-BFGS-B",lower =c(0.01,0.01,0.01), upper =c(0.99,0.99,0.99))
> out
-----------------------------------
*$par
[1] 0.01 0.01 0.01*
[...]
$convergence
[1] 0
*$message
[1] "CONVERGENCE: NORM OF PROJECTED GRADIENT
<PGTOL"*-----------------------------------
I got the Logli from
"http://www-wiwi.uni-regensburg.de/images/institute/vwl/tschernig/lehre/I_Optimization.R"
[[elided Hotmail spam]]
{
c <- PAR[1] # Konstante in GARCH Gleichung
a <- PAR[2:(P+1)] # ARCH Parameter
g <- PAR[(P+2):(P+Q+1)] # GARCH Parameter
n <- length(X) # Stichprobengr??e
h_sq <- rep(var(X),n) # Vektor der bedingten Varianzen (am Anfang:
unbedingte Var.)
ll <- numeric(n) # Vektor der (MINUS) Log Likelihoods pro
Beobachtung
# Unzul?ssige Parameterwerte ausschlie?en (-> Inf als Wert)
if (sum(a)+sum(g)>1) return(NA) # Instabil -> nicht zugelassen
if (any(PAR<0)) return(NA) # Nichtnegativit?t verletzt -> nicht
zugelassen
# Iterativ Bedingte Varianz und minus Likelihood berechnen
for (i in (max(P,Q)+1):n) {
h_sq[i] <- c+sum(X[i-(1:P)]^2*a)+sum(h_sq[i-(1:Q)]*g)
ll[i] <- -0.5*(log(2*pi)+log(h_sq[i])+X[i]^2/h_sq[i]) # minus
Likelihood
}
# Bedingte Varianzen im Global Environment speichern
h_sq <<- h_sq
# Funktionswert = Log Likelihood
return(sum(ll))
}
--
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