R help - Nov 2009 - Sequential MLE on time series with rolling window

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

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.

-- 
Ajay Shah                                      http://www.mayin.org/ajayshah  
ajayshah at mayin.org                            
http://ajayshahblog.blogspot.com
<*(:-? - wizard who doesn't know the answer.