Semiparametric Localized Bandwidth Selection in Kernel Density Estimation
45 Pages Posted: 12 May 2014
Date Written: May 10, 2014
Abstract
Since conventional cross-validation bandwidth selection methods don't work for the case where the data considered are dependent time series, alternative bandwidth selection methods are needed. In recent years, Bayesian based global bandwidth selection methods have been proposed. Our experience shows that the use of a global bandwidth is however less suitable than using a localized bandwidth in kernel density estimation in the case where the data are dependent time series as discussed in an empirical application of this paper. Nonetheless, a difficult issue is how we can consistently estimate a localized bandwidth. In this paper, we propose a semiparametric estimation method, for which we establish an asymptotic theory for the proposed semiparametric estimator. A by-product of this bandwidth estimate is a new sampling-based likelihood approach to hyperparameter estimation. Monte Carlo simulation studies show that the proposed hyperparameter estimation method works very well, and that the proposed bandwidth estimator outperforms its competitors. Applications of the new bandwidth estimator to the kernel density estimation of Eurodollar deposit rate, as well as the S&P 500 daily return under conditional heteroscedasticity, demonstrate the effectiveness and competitiveness of the proposed semiparametric localized bandwidth.
Keywords: hyperparameter estimation; likelihood score; localized bandwidth
JEL Classification: C13, C14, C21
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