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Erscheinungsjahr: 
2024
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[Journal:] AStA Advances in Statistical Analysis [ISSN:] 1863-818X [Volume:] 108 [Issue:] 4 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2024 [Pages:] 705-731
Verlag: 
Springer, Berlin, Heidelberg
Zusammenfassung: 
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.
Schlagwörter: 
Cyclic long memory
Periodicity
Deterministic periodicity
Periodogram
Gegenbauer process
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