Bandwidth selection with a frequency-domain version of the AIC

Abstract

When it comes to estimating an unknown spectral density as simply and reliably as possible, parametric spectral density estimation using AR models and order selection via AIC is the method of choice. In contrast, no standard method has yet emerged for automatic nonparametric spectral density estimation, and there seems to be little willingness to weigh the advantages and disadvantages of different risk functions and the various methods for estimating them on a case-by-case basis, particularly because it is unclear whether the effort is even worthwhile without concrete prior information about the unknown spectral density. As a result, subjective visual methods are still widely used in practice to determine the appropriate smoothing parameter for a nonparametric estimation. This article aims to encourage the increased use of objective automatic methods by presenting evidence that using what is arguably the simplest and most straightforward frequency-domain version of the AIC for the automatic determination of an appropriate bandwidth enables results that are comparable to those obtained using the standard parametric approach. This evidence is based on both real-world time series and synthetic time series with spectral densities of varying complexity.