ESTIMATION IN NONLINEAR REGRESSION WITH HARRIS RECURRENT MARKOV CHAINS

• 成果类型: Article
• 署名作者: Li, Degui; Tjostheim, Dag; Gao, Jiti
• 署名单位: University of York - UK; University of Bergen; Monash University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1379
• 发表日期: 2016
• 页码: 1957-1987
• 关键词: integrated time-series; ASYMPTOTIC THEORY; nonparametric-estimation; models; Consistency; likelihood; inference

摘要

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.