Nonparametric Density Estimation for Positive Time Series
CORE Discussion Paper No. 2006/85
32 Pages Posted: 5 Dec 2006
Date Written: September 22, 2006
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 alpha-mixing process. We derive the mean integrated squarred 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.
Keywords: Gamma kernel, Nonparametric density estimation, Mixing process, Transaction durations, Realised volatility
JEL Classification: C41, C32
Suggested Citation: Suggested Citation