Fourier Analysis of Serial Dependence Measures

Abstract

Classical spectral analysis is based on the discrete Fourier transform of the autocovariances. In this article we investigate the asymptotic properties of new frequency‐domain methods where the autocovariances in the spectral density are replaced by alternative dependence measures that can be estimated by ‐ statistics. An interesting example is given by Kendall's, for which the limiting variance exhibits a surprising behavior.

Keywords: Spectral theory, strictly stationary time series, ‐statistics