A test for second-order stationarity of time series based on unsystematic sub-samples

TL;DR

This paper proposes a novel, flexible test for second-order stationarity in time series using unsystematic sub-samples, with proven asymptotic properties and demonstrated effectiveness on simulated and real data.

Contribution

It introduces a new stationarity test based on random sub-samples, avoiding dyadic constraints and improving detection of local departures from stationarity.

Findings

Test statistic has asymptotic normality for Gaussian and non-Gaussian series.

Bootstrap procedure effectively estimates variance of the test statistic.

Method shows strong finite sample performance in simulations and real data.

Abstract

In this paper, we introduce a new method for testing the stationarity of time series, where the test statistic is obtained from measuring and maximising the difference in the second-order structure over pairs of randomly drawn intervals. The asymptotic normality of the test statistic is established for both Gaussian and a range of non-Gaussian time series, and a bootstrap procedure is proposed for estimating the variance of the main statistics. Further, we show the consistency of our test under local alternatives. Due to the flexibility inherent in the random, unsystematic sub-samples used for test statistic construction, the proposed method is able to identify the intervals of significant departure from the stationarity without any dyadic constraints, which is an advantage over other tests employing systematic designs. We demonstrate its good finite sample performance on both simulated and real data, particularly in detecting localised departure from the stationarity.