Estimation in Nonlinear Regression with Harris Recurrent Markov Chains

Degui Li, Dag Tjostheim, Jiti Gao

Research output: Contribution to journalArticlepeer-review


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 (2001). Some numerical studies including simulation and empirical application are provided to examine the finite sample performance of the proposed approaches and results.
Original languageEnglish
Pages (from-to)1957-1987
Number of pages33
JournalAnnals of Statistics
Issue number5
Publication statusPublished - 1 Jan 2016

Bibliographical note

Date of Acceptance: 26/08/2015. This is an author produced version of a paper accepted for publication in Annals of Statistics. Uploaded in accordance with the publisher's self-archiving policy.

Cite this