A Frequency-Domain NonStationarity Test for dependent data

TL;DR

This paper introduces a new frequency-domain test for nonstationarity in dependent data, effectively distinguishing it from long-memory behavior with improved empirical performance.

Contribution

A novel, parameter-free nonstationarity test based on periodogram analysis across epochs, with analytically tractable limiting distributions.

Findings

Performs favorably compared to existing methods

Accurately distinguishes nonstationarity from long-memory effects

Provides finite-sum chi-squared distribution expressions

Abstract

Distinguishing long-memory behaviour from nonstationarity is challenging, as both produce slowly decaying sample autocovariances. Existing stationarity tests either fail to account for long-memory processes or exhibit poor empirical size, particularly near the boundary between stationarity and nonstationarity. We propose a new, parameter-free testing procedure based on the evaluation of periodograms across multiple epochs. The limiting distributions derived here are obtained under stationarity and nonstationarity assumptions and analytically tractable, expressed as finite sums of weighted independent $\chi^2$ random variables. Simulation studies indicate that the proposed method performs favorably compared to existing approaches.