Nonlinear spectral density estimation: Thresholding the correlogramAAA

Abstract

Traditional kernel spectral density estimators are linear as a function of the sample autocovariance sequence. The purpose of this article is to propose and analyse two new spectral estimation methods that are based on the sample autocovariances in a nonlinear way. The rate of convergence of the new estimators is quantified, and practical issues such as bandwidth and/or threshold choice are addressed. The new estimators are also compared with traditional ones using flat-top lag-windows in a simulation experiment involving sparse time-series models. © 2012 Blackwell Publishing Ltd.