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

Jan Beran (), Jeremy Näscher, Fabian Pietsch and Stephan Walterspacher
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Jan Beran: University of Konstanz
Jeremy Näscher: University of Konstanz
Fabian Pietsch: Asklepios Klinikum Harburg
Stephan Walterspacher: Klinikum Konstanz

AStA Advances in Statistical Analysis, 2024, vol. 108, issue 4, No 1, 705-731

Abstract: 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.

Keywords: Cyclic long memory; Periodicity; Deterministic periodicity; Periodogram; Gegenbauer process (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10182-024-00499-x

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