Loglikelihood function of Dynamic Factor Models

[Gokhan Yildirim]

Dear Statalist,

I have been looking for the loglikelihood function that is used in the dynamic factor model estimation in Stata. I checked the dfactor file provided by Stata, but could not find the exact form of the equation. Can anyone who knows, could share it?

Thank you,

Best wishes,
Gokhan

[Sebastian Kripfganz]

According to the pdf manual:

dfactor writes the specified model as a state-space model and uses sspace to estimate the parameters by maximum likelihood. See Lütkepohl (2005, 619–621) for how to write the DF model in state-space form. See [TS] sspace for the technical details.

Reference:

Lütkepohl, H. 2005. New Introduction to Multiple Time Series Analysis. New York: Springer.

[Gokhan Yildirim]

Thanks for your reply, Sebastian. I used Lutkepohl's loglikelihood function on page 633 (equation 18.4.3), and it seems that it does not match the Stata's computed loglikelihood. I believe it is not an issue of constant term in the likelihood because Lutkepohl's equation includes the constant term. Is there anyone from Stata that would explicitly convey the loglikelihood function for dynamic factor models?
Thanks!

Best wishes,
Gokhan