Nonlinear Regression with Harris Recurrent Markov Chains
AbstractIn 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. We also discuss the estimation of the parameter vector in a conditional volatility function and its asymptotic theory. Furthermore, we apply our results to the nonlinear regression with I(1) processes and establish an asymptotic distribution theory which is comparable to that obtained by Park and Phillips (2001). Some simulation studies are provided to illustrate the proposed approaches and results.
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Bibliographic InfoPaper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 14/12.
Length: 46 pages
Date of creation: Jul 2012
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Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-14 (All new papers)
- NEP-ECM-2012-07-14 (Econometrics)
- NEP-ORE-2012-07-14 (Operations Research)
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"Asymptotics for Nonlinear Transformations of Integrated Time Series,"
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Monash Econometrics and Business Statistics Working Papers
13/11, Monash University, Department of Econometrics and Business Statistics.
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- Jiti Gao & Shin Kanaya & Degui Li & Dag Tjøstheim, 2013. "Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series," CREATES Research Papers 2013-29, School of Economics and Management, University of Aarhus.
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Cowles Foundation Discussion Papers
1657, Cowles Foundation for Research in Economics, Yale University.
- Park, Joon Y & Phillips, Peter C B, 2001.
"Nonlinear Regressions with Integrated Time Series,"
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- Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
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- Myklebust, Terje & Karlsen, Hans Arnfinn & Tjøstheim, Dag, 2012. "Null Recurrent Unit Root Processes," Econometric Theory, Cambridge University Press, vol. 28(01), pages 1-41, February.
- Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155, October.
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