A proof of consistency of the MLE for nonlinear Markov-switching AR processes
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2022
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Elsevier
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We propose a new approach to demonstrate the consistency of the maximum likelihood estimator for nonlinear Markov-switching AR processes (abbreviated MS-NAR). We obtain a uniform exponential memory loss property for the prediction filter by approximating it by a filter with finite memory. From the -mixing property for the MS-NAR process we obtain an ergodic theorem. Finally, we show that in the linear and Gaussian case our assumptions are fully satisfied.
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NONLINEAR AUTOREGRESSIVE PROCESS, MARKOV SWITCHING, ASYMPTOTIC NORMALITY, CONSISTENCY, HIDDEN MARKOV CHAIN