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Testing for Stationarity in Multivariate Locally Stationary Processes

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  • Ruprecht Puchstein
  • Philip Preuß

Abstract

type="main" xml:id="jtsa12133-abs-0001"> In this article, we propose a nonparametric procedure for validating the assumption of stationarity in multivariate locally stationary time series models. We develop a bootstrap-assisted test based on a Kolmogorov–Smirnov-type statistic, which tracks the deviation of the time-varying spectral density from its best stationary approximation. In contrast to all other nonparametric approaches, which have been proposed in the literature so far, the test statistic does not depend on any regularization parameters like smoothing bandwidths or a window length, which is usually required in a segmentation of the data. We additionally show how our new procedure can be used to identify the components where non-stationarities occur and indicate possible extensions of this innovative approach. We conclude with an extensive simulation study, which shows finite-sample properties of the new method and contains a comparison with existing approaches.

Suggested Citation

  • Ruprecht Puchstein & Philip Preuß, 2016. "Testing for Stationarity in Multivariate Locally Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 3-29, January.
    • Handle: RePEc:bla:jtsera:v:37:y:2016:i:1:p:3-29
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    File URL: http://hdl.handle.net/10.1111/jtsa.12133
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    References listed on IDEAS

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    2. Tata Subba Rao & Granville Tunnicliffe Wilson & Soutir Bandyopadhyay & Carsten Jentsch & Suhasini Subba Rao, 2017. "A Spectral Domain Test for Stationarity of Spatio-Temporal Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 326-351, March.
    3. Rajae Azrak & Guy Mélard, 2022. "Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches," Stats, MDPI, vol. 5(3), pages 1-21, August.

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