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Combining Cumulative Sum Change‐Point Detection Tests for Assessing the Stationarity of Univariate Time Series
Author(s) -
Bücher Axel,
Fermanian JeanDavid,
Kojadinovic Ivan
Publication year - 2019
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12431
Subject(s) - univariate , series (stratigraphy) , resampling , consistency (knowledge bases) , monte carlo method , null hypothesis , statistical hypothesis testing , mathematics , rank (graph theory) , asymptotic distribution , cumulative distribution function , asymptotic analysis , statistics , empirical distribution function , econometrics , probability density function , multivariate statistics , paleontology , geometry , combinatorics , estimator , biology
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 datasets are provided. Extensions to multi‐variate time series are briefly discussed as well.