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st: Positive log likelihood values in a switching regression


From   Anil Caliskan <acaliska@gmu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Positive log likelihood values in a switching regression
Date   Fri, 14 Sep 2007 12:32:42 -0400

Dear Stata list:

I am trying to determine a regime switch date using the framework suggested in Goldfeld and Quandt (1973) and applied in Mankiw (1987). The regressions are modeled as below: 

yt = beta01 + beta11*x1t + beta21*t + beta31*t^2 + e1t for t=1,...,i-1
yt = beta02 + beta12*x1t + beta22*t + beta32*t^2 + e2t for t=i,...,N

I ran the regressions for all possible regime switch dates, i's, and calculated the log likelihood based on the formula:

logL=-0.5*N*log(2*pi)-(i-1)*log(sigma1^2)-(N-(i-1))*log(sigma2^2)-0.5*(e1'e1/sigma1^2)-0.5*(e2'e2/sigma2^2)

I obtained e.'e. by using e(rss) and sigma. by using e(rmse) after each regression. 

The likelihood function that I computed is concave, however values are positive, which is the cause of my concern. I would be grateful if you help me understand why I am getting positive instead of negative values and if I am making a mistake.

Thanks in advance.

Anil Caliskan. 



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