Density estimation for nonlinear parametric models with conditional heteroscedasticity

• Published in: Journal of econometrics Vol. 155; no. 1; pp. 71 - 82
• Main Author: Zhao, Zhibiao
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2010; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Applications; Asymptotic methods; Bahadur representation; Bahadur representation Conditional heteroscedasticity Density estimation Fisher information Nonlinear time series Nonparametric kernel density Stationary density Stochastic regression; Conditional heteroscedasticity; Density estimation; Economic models; Estimation; Exact sciences and technology; Fisher information; Inference from stochastic processes; time series analysis; Insurance, economics, finance; Mathematics; Maximum likelihood method; Non-linear models; Nonlinear time series; Nonparametric inference; Nonparametric kernel density; Parameter estimation; Parametric inference; Probability and statistics; Regression analysis; Sciences and techniques of general use; Simulation; Stationarity; Stationary density; Statistics; Stochastic regression; Studies; Time series; Variance; Density estimation; Nonlinear time series; Nonparametric kernel density; C13; C02; Stationary density; Stochastic regression; Bahadur representation; Conditional heteroscedasticity; Fisher information; Parameter estimation; Conditional distribution; Conditional likelihood; Non parametric estimation; Stochastic process; Variance; Parametric method; Stationary series; Lower bound; Non linear estimation; Covariance analysis; Time series; Statistical estimation; Nonlinear problems; Parametric estimation; Variance analysis; Heteroscedasticity; Statistical method; Statistical regression; Simulation; Non linear model; Maximum likelihood; Autocorrelation; Econometrics
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2009.09.013

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.