Testing equality of spectral densities using randomization techniques

TL;DR

This paper introduces a nonparametric randomization-based test for equality of spectral density matrices across multiple stationary processes, demonstrating strong theoretical properties and effective performance in simulations.

Contribution

It proposes a novel $L_2$-type test statistic with randomization methods for critical values, enhancing nonparametric spectral density comparison.

Findings

Asymptotic exactness of the test

High power and accurate size in simulations

Effective for dependent stationary processes

Abstract

In this paper, we investigate the testing problem that the spectral density matrices of several, not necessarily independent, stationary processes are equal. Based on an $L_2$-type test statistic, we propose a new nonparametric approach, where the critical values of the tests are calculated with the help of randomization methods. We analyze asymptotic exactness and consistency of these randomization tests and show in simulation studies that the new procedures posses very good size and power characteristics.