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Nonparametric density estimation for positive time series

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Author Info
BOUEZMARNI, Taoufik
ROMBOUTS, Jeroen V. K.

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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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2006085.

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Date of creation: 01 Oct 2006
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Handle: RePEc:cor:louvco:2006085

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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:
C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
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  1. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November. [Downloadable!] (restricted)
  2. Drost, Feike C & Werker, Bas J M, 2004. "Semiparametric Duration Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 40-50, January.
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  3. 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)
  4. BAUWENS, Luc & VEREDAS, David, 1999. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," CORE Discussion Papers 1999058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  5. 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)
  6. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889. [Downloadable!]
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  7. Marcelo Fernandes & Paulo Monteiro, 2005. "Central limit theorem for asymmetric kernel functionals," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(3), pages 425-442, September. [Downloadable!] (restricted)
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  8. Park, B.U. & Simar, L., 1992. "Efficient Semiparametric Estimation in Stochastic Frontier Model," Papers 9201, Catholique de Louvain - Institut de statistique.
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  9. Ghysels, Eric & Gourieroux, Christian & Jasiak, Joann, 2004. "Stochastic volatility duration models," Journal of Econometrics, Elsevier, vol. 119(2), pages 413-433, April. [Downloadable!] (restricted)
  10. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  11. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April. [Downloadable!] (restricted)
  12. Haldrup, Niels & Nielsen, Morten Orregaard, 2006. "A regime switching long memory model for electricity prices," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 349-376. [Downloadable!] (restricted)
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  13. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280. [Downloadable!] (restricted)
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  14. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
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  15. 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, February. [Downloadable!]
  16. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June. [Downloadable!] (restricted)
  17. 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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  18. 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)
  19. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July. [Downloadable!] (restricted)
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  20. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January. [Downloadable!] (restricted)
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  21. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
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Cited by:
(explanations, 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. 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!]
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  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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