A Robbins-Monro algorithm for non-parametric estimation of NAR process with Markov-Switching: asymptotic normality

TL;DR

This paper develops a Robbins-Monro algorithm for non-parametric estimation of Markov-switching nonlinear autoregressive processes, establishing asymptotic normality and demonstrating its effectiveness through simulations.

Contribution

It introduces a Robbins-Monro based estimation method for MS-NAR processes and proves its asymptotic normality, extending previous work on consistency.

Findings

Proved the asymptotic normality of the estimator.

Validated the estimation procedure through detailed simulations.

Abstract

This paper is the second part of our study on the non-parametric estimation of MS-NAR processes started with [L. Fermin et al. 2017]. We consider the Nadaraya-Watson type regression function estimator for non-linear autoregressive Markov switching processes. In this context the regression function estimator is interpreted as a solution of a local weighted We have introduced, in the first work, a restoration-estimation Robbins-Monro algorithm to approximate the estimator, and we proved identifiability of model and the consistency of the non-parametric estimator. In this work, we obtain the central limit theorem for the non-parametric estimator, whether the Markov chain is observed or not. Finally, we present a detailed simulation study illustrating the performances of our estimation procedure.