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.Comment: 45 pages, 2 figures, 10 table