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Testing for periodicity at an unknown frequency under cyclic long memory, with applications to respiratory muscle training

Author

Listed:
  • Jan Beran

    (University of Konstanz)

  • Jeremy Näscher

    (University of Konstanz)

  • Fabian Pietsch

    (Asklepios Klinikum Harburg)

  • Stephan Walterspacher

    (Klinikum Konstanz
    Witten/Herdecke University (UW/H))

Abstract

A frequent problem in applied time series analysis is the identification of dominating periodic components. A particularly difficult task is to distinguish deterministic periodic signals from periodic long memory. In this paper, a family of test statistics based on Whittle’s Gaussian log-likelihood approximation is proposed. Asymptotic critical regions and bounds for the asymptotic power are derived. In cases where a deterministic periodic signal and periodic long memory share the same frequency, consistency and rates of type II error probabilities depend on the long-memory parameter. Simulations and an application to respiratory muscle training data illustrate the results.

Suggested Citation

  • Jan Beran & Jeremy Näscher & Fabian Pietsch & Stephan Walterspacher, 2024. "Testing for periodicity at an unknown frequency under cyclic long memory, with applications to respiratory muscle training," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(4), pages 705-731, December.
    • Handle: RePEc:spr:alstar:v:108:y:2024:i:4:d:10.1007_s10182-024-00499-x
    DOI: 10.1007/s10182-024-00499-x
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