# Fourier analysis of serial dependence measures

## TL;DR

This paper explores new frequency domain methods for analyzing serial dependence using U-statistics-based measures like Kendall's tau, revealing unique asymptotic properties and behaviors.

## Contribution

It introduces a novel spectral analysis approach replacing auto-covariances with U-statistics dependence measures, expanding spectral analysis tools.

## Key findings

- Kendall's tau-based spectral density exhibits surprising limiting variance behavior
- Asymptotic properties of new frequency domain methods are characterized
- Alternative dependence measures can be effectively used in spectral analysis

## Abstract

Classical spectral analysis is based on the discrete Fourier transform of the auto-covariances. In this paper we investigate the asymptotic properties of new frequency domain methods where the auto-covariances in the spectral density are replaced by alternative dependence measures which can be estimated by U-statistics. An interesting example is given by Kendall{'}s $\tau$ , for which the limiting variance exhibits a surprising behavior.