Nonparametric density estimation for positive time series

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 and realized volatility is provided. Key words: Gamma kernel, Nonparametric density estimation, Mixing process, Transaction durations, Realised volatility. We would like to thank Luc Bauwens, Jean-Marie Rolin for useful comments. HEC Montr

• Type: Journal
• Year: 2010
• Where: CSDA
• Authors: Taoufik Bouezmarni, Jeroen V. K. Rombouts
• Keywords: Cote Sainte Catherine, CSDA 2010, Density Estimator, Gamma Kernel