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
Sequential MLE on time series with rolling window
2 messages · R_help Help, 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.
Ajay Shah http://www.mayin.org/ajayshah ajayshah at mayin.org http://ajayshahblog.blogspot.com <*(:-? - wizard who doesn't know the answer.