Nonlinear Spectral Density Estimation: Thresholding the Correlogram

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.

Keywords: Autocovariance matrix, flat‐top lag‐windows, kernel smoothing, sparsity, thresholding, wavelets