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

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