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

Abstract

We derive tests of stationarity for continuous univariate time series by combining changepoint tests sensitive to changes in the contemporary distribution with tests sensitive to changes in the serial dependence. Rank-based cumulative sum tests based on the empirical distribution function and on the empirical autocopula at a given lag are considered first. The combination of their dependent p-values relies on a joint dependent multiplier bootstrap of the two underlying statistics. Conditions under which the proposed combined testing procedure is asymptotically valid under stationarity are provided. After discussing the choice of the maximum lag to investigate, extensions based on tests solely focusing on second-order characteristics are proposed. The finite-sample behaviors of all the derived statistical procedures 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.