Nonparametric Density Estimation for Positive Time Series

CORE Discussion Paper No. 2006/85

32 Pages Posted: 5 Dec 2006

See all articles by Taoufik Bouezmarni

Taoufik Bouezmarni

HEC Montreal

J. V. K. Rombouts

HEC Montreal; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE); Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE); Center for Interuniversity Research and Analysis on Organization (CIRANO)

Date Written: September 22, 2006

Abstract

The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For i.i.d. data several solutions have been put forward to solve this boundary problem. In this paper we propose the gamma kernel estimator as density estimator for positive data from a stationary alpha-mixing process. We derive the mean integrated squarred error, almost sure convergence and asymptotic normality. In a Monte Carlo study, where we generate data from an autoregressive conditional duration model and a stochastic volatility model, we find that the gamma kernel outperforms the local linear density estimator. An application to data from financial transaction durations, realized volatility and electricity price data is provided.

Keywords: Gamma kernel, Nonparametric density estimation, Mixing process, Transaction durations, Realised volatility

JEL Classification: C41, C32

Suggested Citation

Bouezmarni, Taoufik and Rombouts, Jeroen, Nonparametric Density Estimation for Positive Time Series (September 22, 2006). CORE Discussion Paper No. 2006/85, Available at SSRN: https://ssrn.com/abstract=949156 or http://dx.doi.org/10.2139/ssrn.949156

Taoufik Bouezmarni (Contact Author)

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3
Canada

Jeroen Rombouts

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE) ( email )

Pavillon De Sève
Ste-Foy, Quebec G1K 7P4
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

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