Likelihood-ratio tests for hidden Markov models

We consider hidden Markov models as a versatile class of models for weakly dependent random phenomena. The topic of the present paper is likelihood-ra tio testing for hidden Markov models, and we show that, under appropriate c onditions, the standard asymptotic theory of likelihood-ratio tests is vali d. Such tests are crucial in the specification of multivariate Gaussian hid den Markov models, which we use to illustrate the applicability of our gene ral results. Finally, the methodology is illustrated by means of a real dat a set.