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We deal with the estimation of the regime number in a linear Gaussianautoregressive process with a Markov regime (AR-MR). The problem of estimatingthe number of regimes in this type of series is that of determining the numberof states in the hidden Markov chain controlling the process. We propose amethod based on penalized maximum likelihood estimation and establish itsstrong consistency (almost sure) without assuming previous bounds on the numberof states.

Penalized estimate of the number of states in Gaussian linear AR with Markov regime