We consider nonparametric estimation for functional autoregressive process with Markov switching. First, we study the case where the complete data is available; i.e. when we observe the Markov switching regime, then we estimate the regression function in each regime using a Nadaraya-Watson type estimator. Second, we introduce a nonparametric recursive algorithm in the case of hidden Markov switching regime, which restore the missing data by means Monte-Carlo step and estimate the regression functions by a Robbins-Monro step. Consistency and asymptotic normality of the estimators are proved.
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