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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 independent and identically distributed data, several solutions have been put forward to solve this boundary problem. In this paper, we propose the gamma kernel estimator as a density estimator for positive time series data from a stationary [alpha]-mixing process. We derive the mean (integrated) squared error and asymptotic normality. In a Monte Carlo simulation, we generate data from an autoregressive conditional duration model and a stochastic volatility model. We study the local and global behavior of the estimator and we find that the gamma kernel estimator outperforms the local linear density estimator and the Gaussian kernel estimator based on log-transformed data. We also illustrate the good performance of the h-block cross-validation method as a bandwidth selection procedure. An application to data from financial transaction durations and realized volatility is provided.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 54 (2010)
Issue (Month): 2 (February)
Pages: 245-261

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Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:245-261

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Citations

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Cited by:
  1. 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.
  2. 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).
  3. Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2007. "Nonparametric Density Estimation for Multivariate Bounded Data," Cahiers de recherche 0732, CIRPEE.
  4. 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.
  5. 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.
  6. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.

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