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

TL;DR

This paper develops a Robbins-Monro based recursive algorithm for nonparametric estimation of NAR processes with Markov switching, demonstrating its consistency and effectiveness through theoretical proofs and numerical experiments.

Contribution

It introduces a novel recursive estimation method for hidden Markov switching regimes using Monte Carlo and Robbins-Monro steps, with proven consistency.

Findings

Algorithm achieves consistent estimation in both complete and hidden regimes.

Numerical experiments confirm the effectiveness of the proposed method.

The approach outperforms traditional methods in simulated scenarios.

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.