Journal of Statistical Planning and Inference

Volume 215, December 2021, Pages 109-126

A test for second-order stationarity of a time series based on the maximum of Anderson–Darling statistics

Author links open overlay panelShibin Zhang

Cite

https://doi.org/10.1016/j.jspi.2021.02.010

Highlights

• • Spectral domain-based test for second-order stationarity.

• • The test is easy to program and quite computationally efficient.

• • The test is applicable to extensive types of time series.

Abstract

This paper is concerned with testing the second-order stationarity of a time series. By using a blockwise scheme, the test is transformed to compare local spectra of different segments of the blocked time series. Based on periodogram-ratios of each pair of segments at the same frequency points, an Anderson–Darling-like statistic is constructed to compare their spectra. By maximizing several Anderson–Darling-like statistics, a test statistic is proposed for testing second-order stationarity. Under the null, the probability distribution of the proposed statistic can be approximated by simulation. Extensive simulation examples show that the proposed test approach achieves good performance.

https://doi.org/10.1016/j.jspi.2021.02.010