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Nonparametric Density Estimation for Positive Time Series

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Author Info
Taoufik Bouezmarni
Jeroen V.K. Rombouts () (IEA, HEC Montréal)

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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 ?-mixing process. We derive the mean integrated squared 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.

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File URL: http://www.hec.ca/iea/cahiers/2006/iea0609_jrombouts.pdf
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Publisher Info
Paper provided by HEC Montréal, Institut d'économie appliquée in its series Cahiers de recherche with number 06-09.

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Length: 34 pages
Date of creation: Sep 2006
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Handle: RePEc:iea:carech:0609

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Postal: Institut d'économie appliquée HEC Montréal 3000, Chemin de la Côte-Sainte-Catherine Montréal, Québec H3T 2A7
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Related research
Keywords: Gamma kernel nonparametric density estimation mixing process transaction durations realised volatility.

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Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March. [Downloadable!] (restricted)
  2. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241. [Downloadable!] (restricted)
  3. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, March. [Downloadable!]
  4. Bauwens, L. & Veredas, D., 1999. "The Stochastic Conditional Duration Model: a Latent Factor Model for the Analysis of Financial Durations," Papers 9958, Catholique de Louvain - Center for Operations Research and Economics.
  5. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609. [Downloadable!] (restricted)
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  6. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July. [Downloadable!] (restricted)
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  1. Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2007. "Nonparametric density estimation for multivariate bounded data," Cahiers de recherche 07-10, HEC Montréal, Institut d'économie appliquée. [Downloadable!]
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  2. Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2006. "Density and Hazard Rate Estimation for Censored and ?-mixing Data Using Gamma Kernels," Cahiers de recherche 06-16, HEC Montréal, Institut d'économie appliquée. [Downloadable!]
  3. Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2007. "Semiparametric Multivariate Density Estimation for Positive Data Using Copulas," Cahiers de recherche 07-08, HEC Montréal, Institut d'économie appliquée. [Downloadable!]
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