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Generalizations of the KPSS-test for stationarity. (English) Zbl 1061.62136
Summary: We propose automatic generalizations of the KPSS-test [D. Kwiatkowski, P. C. B. Phillips, P. Schmidt and Y. Shin, J. Econom. 54, 159–178 (1992; Zbl 0871.62100)] for the null hypothesis of stationarity of a univariate time series. We can use these tests for the null hypotheses of trend stationarity, level stationarity and zero mean stationarity. We introduce the asymptotic null distributions and we determine consistency against relevant nonstationary alternatives. We compare the properties of the tests with those of other proposed tests for stationarity. Monte Carlo simulations support the relevance of the tests when an autoregressive process with large positive autocorrelations is likely under the null hypothesis.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C05 Monte Carlo methods
65C60 Computational problems in statistics (MSC2010)
62E20 Asymptotic distribution theory in statistics
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