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A Wavelet‐Based Test for Stationarity

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  • Rainer Von Sachs
  • Michael H. Neumann

Abstract

We develop a test for stationarity of a time series against the alternative of a time‐varying covariance structure. Using localized versions of the periodogram, we obtain empirical versions of a reasonable notion of a time‐varying spectral density. Coefficients with respect to a Haar wavelet series expansion of such a time‐varying periodogram are an indicator of whether there is some deviation from covariance stationarity. We propose a test based on the limit distribution of these empirical coefficients.

Suggested Citation

  • Rainer Von Sachs & Michael H. Neumann, 2000. "A Wavelet‐Based Test for Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(5), pages 597-613, September.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:5:p:597-613
    DOI: 10.1111/1467-9892.00200
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    Cited by:

    1. E A K Cohen & A J Gibberd, 2022. "Wavelet spectra for multivariate point processes [The spectral analysis of point processes]," Biometrika, Biometrika Trust, vol. 109(3), pages 837-851.
    2. Embleton, Jonathan & Knight, Marina I. & Ombao, Hernando, 2022. "Wavelet testing for a replicate-effect within an ordered multiple-trial experiment," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    3. Kley, Tobias & Preuss, Philip & Fryzlewicz, Piotr, 2019. "Predictive, finite-sample model choice for time series under stationarity and non-stationarity," LSE Research Online Documents on Economics 101748, London School of Economics and Political Science, LSE Library.

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