ASYMPTOTIC NULL DISTRIBUTION OF THE LIKELIHOOD RATIO TEST IN MARKOV SWITCHING MODELS

Markov switching (MS) models raise a problem known as testing hypothes es when a nuisance parameter is not identified under the null hypothes is. I show that the asymptotic distribution theory used for testing in presence of such a problem appears to work also for MS models, even t hough its validity can be questioned because of identically zero score s under the null estimates. Assuming the validity of this distribution theory, I derive the asymptotic null distribution of the likelihood r atio (LR) test for various MS models. Monte Carlo experiments show tha t the LR asymptotic distributions approximate the empirical distributi ons very well.