Optimal Bandwidth Selection in Non-Parametric Spectral Density Estimation: Review and Simulation

Abstract: This paper deals with optimal window width choice in non-parametric lag- or spectral window estimation of the spectral density of a stationary zero-mean process. Several approaches are reviewed: the cross-validation based methods describedby Hurvich (1985), Beltrao & Bloomfield (1987) and Hurvich & Beltrao (1990), an iterative procedure due to Bühlmann (1996), and a bootstrap approach followed by Franke & Härdle (1992). These methods are compared in terms of the mean square error, the mean square percentage error, and a third measure of distance between the true spectral density and its estimate. The comparison is based on a small simulation study. The processes that are simulated are in the class of ARMA (5,5) processes. Based on the simulation evidence, we suggest to use a slightly modified version of Bühlmann's (1996) iterative method.