Sequential MLE on time series with rolling window

[R_help Help]

Hi,

Assuming I have a time series on which I will perform rolling-window
MLE. In other words, if I stand at time t, I'm using points t-L+1 to t
for my MLE estimate of parameters at time t (here L is my rolling
window width). Next, at t+1, I'll do the same.

My question is that is there anyway to avoid performing MLE each time
like does the above. My impression is that rolling from point t to
t+1, the likelihood function is equivalent to cutting out point t-L+1
and add back likelihood at point t+1. Is there any smart way to
sequentially update the MLE instead of brute force calculation every
time? Any suggestion or reference would be appreciated. Thank you.

rc

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[Ajay Shah]

On Tue, Nov 03, 2009 at 11:54:52PM -0500, R_help Help wrote:

> Hi,
>
> Assuming I have a time series on which I will perform rolling-window
> MLE. In other words, if I stand at time t, I'm using points t-L+1 to t
> for my MLE estimate of parameters at time t (here L is my rolling
> window width). Next, at t+1, I'll do the same.
>
> My question is that is there anyway to avoid performing MLE each time
> like does the above. My impression is that rolling from point t to
> t+1, the likelihood function is equivalent to cutting out point t-L+1
> and add back likelihood at point t+1. Is there any smart way to
> sequentially update the MLE instead of brute force calculation every
> time? Any suggestion or reference would be appreciated. Thank you.

One thing you can certainly do is: Take the optimal parameter vector
obtained using observations n to n+T and use it as the starting value
for estimation from observations (n+1) to (n+T+1). The two $\hat theta$
values should be similar to each other, hence just one or two
iterations should be required in making each step.

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<*(:-? - wizard who doesn't know the answer.

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