Likelihood-ratio tests for hidden Markov models

Paolo Guidici, Tobias Rydén and Pierre Vandekerkhove

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,

ISSN 0281-1944

We consider hidden Markov models as a versatile class of models for weakly dependent random phenomena. The topic of the present paper is likelihood-ratio testing for hidden Markov models, and we show that under appropriate conditions the standard asymptotic theory of likelihood-ratio tests is valid. Such tests are crucial in the specification of hidden Markov graphical Gaussian models, which we use to illustrate the applicability of our general results. Finally, our methodology is illustrated by means of a real data-set.
Key words:
hidden multivariate Markov models, likelihood-ratio tests, temporal graphical models