Nonparametric Localized Bandwidth Selection for Kernel Density Estimation

As conventional cross-validation bandwidth selection methods do not work properly in the situation where the data are serially dependent time series, alternative bandwidth selection methods are necessary. In recent years, Bayesian based methods for global bandwidth selection have been studied. Our experience shows that a global bandwidth is however less suitable than a localized bandwidth in kernel density estimation based on serially dependent time series data. Nonetheless, a difficult issue is how we can consistently estimate a localized bandwidth. This paper presents a nonparametric localized bandwidth estimator, for which we established a completely new asymptotic theory. Applications of this new bandwidth estimator to the kernel density estimation of Eurodollar deposit rate and the S&P 500 daily return demonstrate the effectiveness and competitiveness of the proposed localized bandwidth.