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Nonparametric density estimation for positive time series

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  • BOUEZMARNI, Taoufik
  • ROMBOUTS, Jeroen V. K.

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: 00 Oct 2006
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Handle: RePEc:cor:louvco:2006085

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Keywords: gamma kernel; nonparametric density estimation; mixing process; transaction durations; realised volatility;

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Citations

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Cited by:
  1. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K., 2007. "Semiparametric multivariate density estimation for positive data using copulas," CORE Discussion Papers 2007054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Peter Malec & Melanie Schienle, 2012. "Nonparametric Kernel Density Estimation Near the Boundary," SFB 649 Discussion Papers SFB649DP2012-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K., 2007. "Nonparametric density estimation for multivariate bounded data," CORE Discussion Papers 2007065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
  6. Golyandina, Nina & Pepelyshev, Andrey & Steland, Ansgar, 2012. "New approaches to nonparametric density estimation and selection of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2206-2218.

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