A Robbins Monro algorithm for nonparametric estimation of NAR process with Markov-Switching: consistency
Statistics Theory
2017-04-25 v6 Statistics Theory
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.
Cite
@article{arxiv.1407.3747,
title = {A Robbins Monro algorithm for nonparametric estimation of NAR process with Markov-Switching: consistency},
author = {Lisandro Fermín and Ricardo Ríos and Luis-Angel Rodríguez},
journal= {arXiv preprint arXiv:1407.3747},
year = {2017}
}