[R-SIG-Finance] GARCH estimation

[Patrick Burns]

Putting box constraints on the parameters is probably
a good idea, but if I read the objective correctly, I don't
think that will guarantee 'ht' will always be positive.

Pat

Joshua Reich wrote:

>Why not use the L-BFGS-B method and supply a lower bound argument?
>
>Josh
>
>-----Original Message-----
>From: r-sig-finance-bounces at stat.math.ethz.ch
>[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Patrick
>Burns
>Sent: Wednesday, December 05, 2007 12:04 PM
>To: ShyhWeir Tzang
>Cc: r-sig-finance at stat.math.ethz.ch
>Subject: Re: [R-SIG-Finance] GARCH estimation
>
>You need to do something in the event that ht
>becomes non-positive.  For example, something
>like:
>
>if(ht <= 0) ht <- 1e-10
>
>What number you use will depend on what the
>reasonable range of values is for the particular
>problem.
>
>Patrick Burns
>patrick at burns-stat.com
>+44 (0)20 8525 0696
>http://www.burns-stat.com
>(home of S Poetry and "A Guide for the Unwilling S User")
>
>ShyhWeir Tzang wrote:
>
>  
>
>>Dear all:
>>
>>I have a garch equation different from the traditional one:
>>
>>y(t)=b1+b2*x(t) + sqrt(h(t))*z(t), where z(t)~N(0,1)
>>    
>>
>h(t)=b3+b4*h(t-1)+b5*(
>  
>
>>z(t-1)-b6*sqrt(h(t-1) )^2
>>
>>I tried to use optim to estimate the six parameters:
>>
>>garch <- function(b,x,y){
>>        b1<-b[1]
>>        b2<-b[2]
>>        b3<-b[3]
>>        b4<-b[4]
>>        b5<-b[5]
>>        b6<-b[6]
>>        N<-length(y)
>>        lkhd<-0
>>        ht<-var(y)
>>        for (i in 1:N){
>>               zt<-y[i]-b1-b2*x[i]
>>               ht<-b3+b4*(ht)^2+b5*(zt/sqrt(ht)-b6*sqrt(ht))^2
>>               lkhd<-lkhd +log(ht)+zt^2/ht
>>               }
>>       return(lkhd)
>>}
>>optim(c(0.01,0.2,0.2,0.2,0.2,0.2),method="BFGS",fn=garch,
>>   x=data.x,y=data.y)
>>
>>However, I got the following warnings:
>>In log(ht) : create NaNs
>>In sqrt(ht) : create NaNs
>>........................
>>
>>Can anyone help me interpreting these warnings? Are there any other
>>    
>>
>better
>  
>
>>way to estimate the parameters? Thank you very much.
>>
>>ShyhWeir
>>
>>	[[alternative HTML version deleted]]
>>
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>> 
>>
>>    
>>
>
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