Stability of a characterization by the identical distribution of linear forms

Hidden Markov models (HMMs) have during the last decade become a widely spread tool for modelling sequences of dependent random variables. Inference for HMMs has been considered by several authors, but so far no work has been done on estimating their order. In this paper we propose a penalized likelihood estimator for this purpose. This estimator is based on the m-dimensional distribution of HMM, and it is shown that in the limit it does not underestimate the order.