The order estimation for hidden Markov models

The hidden Markov model has been successfully applied to many fields. In this paper, we provide a novel method to estimate the order of finite state stationary hidden Markov models. Our method relies on the fact that return times of a fixed observation are identical distribution if starting points correspond to the unique hidden state. We obtain the order estimator by clustering all return times of different starting points, and prove that the estimator is strong consistent. The results of numerical experiments show that the proposed method has a better performance compared to the previous, its accuracy is greatly improved, and its computational complexity is significantly reduced. Finally, we give the application of our method to a real-life data set. (C) 2019 Elsevier B.V. All rights reserved.