Combining cumulative sum change-point detection tests for assessing the stationarity of univariate time series
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Date
2017
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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.
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Keywords
copula, dependent p-value combination, multiplier bootstrap, rank-based statistics, tests of stationarity