Estimation of the Evolutionary Spectra with Application to Stationarity Test

TL;DR

This paper introduces an improved method for estimating the evolutionary spectral density of non-stationary processes, addressing bias issues, and proposes a new stationarity test based on these estimates, with practical experimental validation.

Contribution

It develops a novel evolutionary spectral density estimator using multitaper techniques and introduces a non-parametric stationarity test based on these estimates.

Findings

Enhanced spectral density estimates with reduced bias leakage

Effective non-parametric stationarity testing method

Validated through comprehensive experimental studies

Abstract

In this work, we propose a new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley. Among various frameworks of modeling non-stationary processes, the distinguishing feature of the evolutionary spectra is its focus on the physical meaning of frequency. The classical estimate of the evolutionary spectral density is based on a double-window technique consisting of a short-time Fourier transform and a smoothing. However, smoothing is known to suffer from the so-called bias leakage problem. By incorporating Thomson's multitaper method that was originally designed for stationary processes, we propose an improved estimate of the evolutionary spectral density, and analyze its bias/variance/resolution tradeoff. As an application of the new estimate, we further propose a non-parametric rank-based stationarity test, and provide various experimental studies.