A Robbins-Monro algorithm for non-parametric estimation of NAR process with Markov-Switching: asymptotic normality
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.
Cite
@article{arxiv.2603.29440,
title = {A Robbins-Monro algorithm for non-parametric estimation of NAR process with Markov-Switching: asymptotic normality},
author = {Lisandro Fermin and Ricardo Rios and Luis-Ángel Rodríguez},
journal= {arXiv preprint arXiv:2603.29440},
year = {2026}
}