A time varying hidden Markov model with latent information

摘要

The time varying hidden Markov models are based on the use of some observable variables,which we suppose to drive the transition probabilities. The estimation of the model is conditional on the availability of this information, which is not obvious. In this paper we propose a time varying hidden Markov model with the transition probabilities driven by a latent variable subject to the same Markovian changes of the dependent variable. The model has a state-space form and the latent variable is estimated using a modified Kim filter, so that this information is always available; furthermore, the estimation of this latent variable is useful to forecast the changes in the state. We show the practical characteristics of this model through an example in which the latent variable is the business cycle.