Identiability and Inference of Hidden Markov Models
Yonghong An, Yingyao Hu, Matt Shum · 2013
This paper considers the identiability of a class of hidden Markov models where both the observed and unobserved components take values in nite spaces X andY, respectively. We prove that both the Markov transition probability and the conditional probability are identied from the joint distribution of three consecutive variables given that the cardinality ofX is not greater than that ofY. The approach of identication provides a novel methodology to estimate the hidden Markov models, and the performance of the proposed estimators is illustrated by a Monte Carlo experiment. We further extend our methodology to the Markov-switching model which generalizes the hidden Markov model, and show that the extended model can be similarly identied and estimated from the joint distribution of four consecutive variables if the cardinalities ofY andX are equal.