Estimation in nonlinear regression with Harris recurrent Markov chains

TL;DR

This paper develops asymptotic theory for nonlinear least squares estimators in nonlinear regression models driven by Harris recurrent Markov chains, highlighting the influence of chain properties on convergence rates.

Contribution

It introduces a novel asymptotic framework for nonlinear regression with Harris recurrent Markov chains, extending existing results to more general dependence structures.

Findings

Convergence rates depend on the number of regenerations of the Markov chain.

Asymptotic distribution theory is derived for models with $I(1)$ processes.

Numerical studies demonstrate the finite sample performance of the estimators.

Abstract

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov chain. Furthermore, we discuss the estimation of the parameter vector in a conditional volatility function, and apply our results to the nonlinear regression with $I(1)$ processes and derive an asymptotic distribution theory which is comparable to that obtained by Park and Phillips [Econometrica 69 (2001) 117-161]. Some numerical studies including simulation and empirical application are provided to examine the finite sample performance of the proposed approaches and results.