Combining cumulative sum change-point detection tests for assessing the stationarity of univariate time series

TL;DR

This paper introduces a new method for testing stationarity in univariate time series by combining change-point detection tests that focus on distributional and dependence changes, validated through simulations and real data.

Contribution

It proposes a novel approach to combine dependent change-point tests for stationarity assessment, including rank-based and second-order characteristic tests, with theoretical validation and practical illustrations.

Findings

The combined tests effectively detect stationarity changes in simulations.

The methods perform well on real-world data sets.

Extensions to multivariate series are feasible.

Abstract

We derive tests of stationarity for univariate time series by combining change-point tests sensitive to changes in the contemporary distribution with tests sensitive to changes in the serial dependence. The proposed approach relies on a general procedure for combining dependent tests based on resampling. After proving the asymptotic validity of the combining procedure under the conjunction of null hypotheses and investigating its consistency, we study rank-based tests of stationarity by combining cumulative sum change-point tests based on the contemporary empirical distribution function and on the empirical autocopula at a given lag. Extensions based on tests solely focusing on second-order characteristics are proposed next. The finite-sample behaviors of all the derived statistical procedures for assessing stationarity are investigated in large-scale Monte Carlo experiments and illustrations on two real data sets are provided. Extensions to multivariate time series are briefly discussed as well.