Harris recurrent Markov chains and nonlinear monotone cointegrated models

TL;DR

This paper investigates a nonlinear cointegration model involving Harris recurrent Markov chains, proposing a nonparametric estimation method for the monotone function and establishing its consistency and convergence rates.

Contribution

It introduces a nonparametric least squares estimator for the monotone function in cointegration models with Harris recurrent Markov chains, along with new Glivenko-Cantelli type results for null recurrent chains.

Findings

Estimator is strongly consistent under mild conditions.

Established convergence rates for the nonparametric estimator.

Proved new Glivenko-Cantelli type results for null recurrent Markov chains.

Abstract

In this paper, we study a nonlinear cointegration-type model of the form \(Z_t = f_0(X_t) + W_t\) where \(f_0\) is a monotone function and \(X_t\) is a Harris recurrent Markov chain. We use a nonparametric Least Square Estimator to locally estimate \(f_0\), and under mild conditions, we show its strong consistency and obtain its rate of convergence. New results (of the Glivenko-Cantelli type) for localized null recurrent Markov chains are also proved.