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arXiv · 1407.3747

A Robbins Monro algorithm for nonparametric estimation of NAR process with Markov-Switching: consistency

Lisandro Fermín·Ricardo Ríos·Luis-Angel Rodríguez
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Abstract

We consider nonparametric estimation for functional autoregressive processes with Markov switching. First, we study the case where 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. Our algorithm restores the missing data by means of a Monte-Carlo step and estimate the regression function via a Robbins-Monro step. Consistency of the estimators are proved in both cases. Finally, we present some numerical experiments on simulated data illustrating the performances of our nonparametric estimation procedure.

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Lisandro Fermín, Ricardo Ríos, Luis-Angel Rodríguez. 2014-07-14. A Robbins Monro algorithm for nonparametric estimation of NAR process with Markov-Switching: consistency. https://doi.org/10.1111/jtsa.12237

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