Estimation in nonlinear regression with Harris recurrent Markov chains

Degui Li, Dag Tjostheim, Jiti Gao

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5 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1957-1987
Number of pages31
JournalAnnals of Statistics
Volume44
Issue number5
DOIs
Publication statusPublished - 1 Oct 2016

Keywords

  • Asymptotic distribution
  • Asymptotically homogeneous function
  • Harris recurrence
  • Integrable function
  • Least squares estimation
  • Nonlinear regression
  • β-null recurrent Markov chain

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