Statistical Modelling 8 (2008), 347–366
A time varying hidden Markov model with latent information
Edoardo Otranto
Dipartimento di Economia, Impresa e Regolamentazione
University of Sassari
Via Torre Tonda 34
I–07100 Sassari
Italy
eotranto@uniss.it
Abstract:
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.
Keywords:
forecasts; latent variables; Markov switching; signal extraction; state-space
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