Asymptotic properties of autoregressive regime-switching models
The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (independent regime switches). In this framework,...