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.
Likelihood with Time-Varying Variances
Re: Likelihood?
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
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