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Testing for cycles in multiple time series

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  • Werner Ploberger
  • Erhard Reschenhofer

Abstract

In practice, it is often impossible to assess the validity of the smoothness assumptions crucial to standard tests for singularities in the spectrum. We therefore propose new tests which are completely insensitive to sharp peaks in the absolutely continuous part of the spectrum. Using Neyman Pearson tests of Bayesian mixtures we first derive admissible tests under simplifying assumptions and then show that under realistic assumptions our test statistics remain the same. The tests are designed to have high power especially against alternatives containing oscillations which are positively correlated with each other. Motivated by a biological dataset with non‐sinusoidal oscillations, we finally extend our approach by including higher harmonics.

Suggested Citation

  • Werner Ploberger & Erhard Reschenhofer, 2010. "Testing for cycles in multiple time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 427-434, November.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:6:p:427-434
    DOI: 10.1111/j.1467-9892.2010.00675.x
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    Cited by:

    1. Reschenhofer, Erhard & Lingler, Michaela, 2013. "Detecting synchronous cycles in financial time series of unequal length," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 1-9.
    2. Erhard Reschenhofer & Werner Ploberger & Georg Lehecka, 2014. "Detecting fuzzy periodic patterns in futures spreads," Statistical Papers, Springer, vol. 55(2), pages 487-496, May.
    3. Erhard Reschenhofer & Manveer Kaur Mangat & Christian Zwatz & Sándor Guzmics, 2020. "Evaluation of current research on stock return predictability," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 334-351, March.

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