R help - Mar 2006 - mle.

hi all,

suppose I have:

r[i] ~ N(0, h[i])
h[i] = a + b*r[i-1] + c*h[i-1] for all i=2..........n

I want to get estimates of a, b, c by mle.

Can you tell me how to do that?


thanks in advance,
Arun

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Arun Kumar Saha <arun.kumar.saha <at> gmail.com> writes:
> 
> hi all,
> 
> suppose I have:
> 
> r[i] ~ N(0, h[i])
> h[i] = a + b*r[i-1] + c*h[i-1] for all i=2..........n
> 
> I want to get estimates of a, b, c by mle.
> 
> Can you tell me how to do that?
> 
  (1) can you convince us this isn't a homework problem?
(a little bit more context would be nice in any case)
  (2) are both r and h observed? if so, then
your (negative log-)likelihood function can use
something along the lines of 
-sum(dnorm(r,mean=...,sd=...,log=FALSE))-sum(dnorm(h,mean=...,sd=...,log=FALSE))
where you fill in the predicted mean and std. dev. of each.

  Ben Bolker