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A new non-parametric stationarity test of time series in the time domain

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  • Lei Jin
  • Suojin Wang
  • Haiyan Wang

Abstract

type="main" xml:id="rssb12091-abs-0001"> 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.

Suggested Citation

  • Lei Jin & Suojin Wang & Haiyan Wang, 2015. "A new non-parametric stationarity test of time series in the time domain," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(5), pages 893-922, November.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:5:p:893-922
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    File URL: http://hdl.handle.net/10.1111/rssb.2015.77.issue-5
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    Citations

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    Cited by:

    1. Axel Bücher & Holger Dette & Florian Heinrichs, 2020. "Detecting deviations from second-order stationarity in locally stationary functional time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1055-1094, August.
    2. Lei Jin & Suojin Wang, 2016. "A New Test for Checking the Equality of the Correlation Structures of two time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 355-368, May.
    3. Garcimartin, Carlos & Kvedaras, Virmantas & Rivas, Luis, 2016. "Business cycles in a balance-of-payments constrained growth framework," Economic Modelling, Elsevier, vol. 57(C), pages 120-132.
    4. Tata Subba Rao & Granville Tunnicliffe Wilson & Alessandro Cardinali & Guy P. Nason, 2017. "Locally Stationary Wavelet Packet Processes: Basis Selection and Model Fitting," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 151-174, March.

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