Density estimation for nonlinear parametric models with conditional heteroscedasticity

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)71-82
Number of pages12
JournalJournal of Econometrics
Volume155
Issue number1
DOIs
StatePublished - Mar 1 2010

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Density estimation
Conditional heteroscedasticity
Parametric model
Parameter estimation
Dependence structure
Lower bounds
Simulation
Maximum likelihood
Time series models
Nonlinear time series

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Cite this

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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 Cram{\'e}r-Rao lower bound. The performance of our density estimate is studied by simulations.",
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Density estimation for nonlinear parametric models with conditional heteroscedasticity. / Zhao, Zhibiao.

In: Journal of Econometrics, Vol. 155, No. 1, 01.03.2010, p. 71-82.

Research output: Contribution to journalArticle

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AB - 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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