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arXiv · 2603.29440

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

Lisandro Fermin·Ricardo Rios·Luis-Ángel Rodríguez
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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.

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Lisandro Fermin, Ricardo Rios, Luis-Ángel Rodríguez. 2026-03-31. A Robbins-Monro algorithm for non-parametric estimation of NAR process with Markov-Switching: asymptotic normality. https://arxiv.org/abs/2603.29440

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