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A new non‐parametric stationarity test of time series in the time domain
Author(s) -
Jin Lei,
Wang Suojin,
Wang Haiyan
Publication year - 2015
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12091
Subject(s) - asymptotic distribution , series (stratigraphy) , mathematics , consistency (knowledge bases) , parametric statistics , test statistic , statistic , sequence (biology) , statistical hypothesis testing , selection (genetic algorithm) , statistics , computer science , estimator , paleontology , genetics , geometry , artificial intelligence , biology
Summary We propose a new double‐order selection test for checking second‐order stationarity of a time series. To develop the test, a sequence of systematic samples is defined via Walsh functions. Then the deviations of the autocovariances based on these systematic samples from the corresponding autocovariances of the whole time series are calculated and the uniform asymptotic joint normality of these deviations over different systematic samples is obtained. With a double‐order selection scheme, our test statistic is constructed by combining the deviations at different lags in the systematic samples. The null asymptotic distribution of the statistic proposed is derived and the consistency of the test is shown under fixed and local alternatives. Simulation studies demonstrate well‐behaved finite sample properties of the method proposed. Comparisons with some existing tests in terms of power are given both analytically and empirically. In addition, the method proposed is applied to check the stationarity assumption of a chemical process viscosity readings data set.