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Nonparametric Density Estimation for Positive Time Series

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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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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
Handle: RePEc:iea:carech:0609
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Institut d'économie appliquée HEC Montréal 3000, Chemin de la Côte-Sainte-Catherine Montréal, Québec H3T 2A7

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