The RATS Software Forum

Dear Tom,

In an MS-VAR (eev_mcmc.rpf), i would like to test for the number of regimes. I was wondering whether I should use the option RESTRICT or instead calculate the LR test statistic (using the command %MSSysRegProb to compute the likelihood values?), after having estimated an MS-VAR with different regimes. In any case, the test statistic would be distributed with a mixture of distributions, which is why it may not converge to a standard (asymptotic) CHI-SQUARE distribution. Then, one solution is perhaps simulate the critical values Monte Carlo simulation. I would appreciate if you could provide me with some programming tips on this issue.

Many thanks indeed.

Kind regards

MCMC isn't going to give you an LR test. You would need to use an ML estimation for that.

There is no method for formally testing the number of regimes that isn't extremely complicated. However, you can use the BIC; it's not quite as formal but should generally give the correct decision. In practice, though, it's often very hard to overfit the number of regimes since the model isn't identified. Plus, the number of parameters added by another regime can be so large that you would only pass a formal test if the LR is really big.

Hi Tom again,

Many thanks indeed for your prompt reply.

Just to clarify. The BIC (like an LR test statistic) also requires knowledge about the likelihood value. Or should I use instead the determinant of the variance and covariance matrix of the estimated residuals? However, the latter can only be used when certain conditions (normality) are met.

Kindly advise me.

Regards.

I don't know of any way to estimate a MS model that avoids making an distributional assumption. You have to be able to compute the probability of the mixture which requires a density function for the data conditional on the regime.