Estimation of the Spectral Density Function in the Presence of Harmonic Components

Abstract

Consider a stationary process of the formXt= Yt+ Zt, whereYtis a linear process with a continuous spectrum, andZtis a finite sum of harmonic components. We discuss two methods of estimating the spectral density function ofYt.In one method we first estimate the autocovariance function ofYtby “correcting” the sample autocovariance function ofXt, and then form the usual “smoothed” Fourier transform. In the other approach, we estimate the spectral density function directly from the autocovariance function ofXtby using the “double weight function” technique.