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Likelihood with Time-Varying Variances

Posted: Wed Oct 13, 2010 3:11 pm
by luching
I have VAR with stochastic volatility of the form

Y_t=X_t*beta + u_t; where V(u_t)=Sigma_t

Is there an inbuilt way to compute the following likelihood?

L(Y^T|beta,Sigma^T);

where Sigma^T is the entire history of Sigma's. Say, Sigma_t is multivariate normal.

Re: Likelihood?

Posted: Thu Oct 14, 2010 9:43 am
by TomDoan
Something like:

sstats start end %logdensity(sigma(t),u(t))>>logl

That would have SIGMA as a SERIES[SYMM] and U as a SERIES[VECT]. If it's more convenient to organize the residuals as a VECT[SERIES], you would do

sstats start end %logdensity(sigma(t),%xt(u,t))>>logl