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Density estimation for nonlinear parametric models with conditional heteroscedasticity

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  • Zhao, Zhibiao

Abstract

This article studies density and parameter estimation problems for nonlinear parametric models with conditional heteroscedasticity. We propose a simple density estimate that is particularly useful for studying the stationary density of nonlinear time series models. Under a general dependence structure, we establish the root n consistency of the proposed density estimate. For parameter estimation, a Bahadur type representation is obtained for the conditional maximum likelihood estimate. The parameter estimate is shown to be asymptotically efficient in the sense that its limiting variance attains the Cramér-Rao lower bound. The performance of our density estimate is studied by simulations.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 155 (2010)
Issue (Month): 1 (March)
Pages: 71-82

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Handle: RePEc:eee:econom:v:155:y:2010:i:1:p:71-82

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Bahadur representation Conditional heteroscedasticity Density estimation Fisher information Nonlinear time series Nonparametric kernel density Stationary density Stochastic regression;

References

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  1. Jian-Feng Yao, 2000. "On Least Squares Estimation for Stable Nonlinear AR Processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(2), pages 316-331, June.
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Cited by:
  1. Yin Liao & John Stachurski, 2011. "Parametric Conditional Monte Carlo Density Estimation," ANU Working Papers in Economics and Econometrics 2011-562, Australian National University, College of Business and Economics, School of Economics.
  2. Zhao, Zhibiao, 2011. "Nonparametric model validations for hidden Markov models with applications in financial econometrics," Journal of Econometrics, Elsevier, vol. 162(2), pages 225-239, June.

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