Nonlinear Regression with Harris Recurrent Markov Chains
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. 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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- Joon Y. Park & Peter C.B. Phillips, 1998.
"Nonlinear Regressions with Integrated Time Series,"
Cowles Foundation Discussion Papers
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"Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series,"
CREATES Research Papers
2013-29, Department of Economics and Business Economics, Aarhus University.
- Gao, Jiti & Kanaya, Shin & Li, Degui & Tjøstheim, Dag, 2015. "Uniform Consistency For Nonparametric Estimators In Null Recurrent Time Series," Econometric Theory, Cambridge University Press, vol. 31(05), pages 911-952, October.
- Jiti Gao & Degui Li & Dag Tjøstheim, 2011. "Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series," Monash Econometrics and Business Statistics Working Papers 13/11, Monash University, Department of Econometrics and Business Statistics.
- Jiti Gao & Degui Li & Dag Tjostheim, 2009. "Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series," School of Economics Working Papers 2009-26, University of Adelaide, School of Economics.
- 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.
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- Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
- Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
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