Testing temporal constancy of the spectral structure of a time series

TL;DR

This paper introduces a nonparametric statistical test to determine if a time series has a constant spectral structure over time, by comparing local and global spectral density estimates.

Contribution

It develops a new nonparametric test for stationarity that detects smoothly time-varying spectral characteristics in stochastic processes.

Findings

Asymptotic properties of the estimators are derived.

The test effectively detects time-varying spectral structures.

Behavior under fixed alternatives is analyzed.

Abstract

Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly time-varying spectral structure. The test is based on a comparison between the sample spectral density calculated locally on a moving window of data and a global spectral density estimator based on the whole stretch of observations. Asymptotic properties of the nonparametric estimators involved and of the test statistic under the null hypothesis of stationarity are derived. Power properties under the alternative of a time-varying spectral structure are discussed and the behavior of the test for fixed alternatives belonging to the locally stationary processes class is investigated.