On randomly periodic strongly dependent time series, with applications to neural respiratory drive data

Jan Beran, Jeremy Näscher and Stephan Walterspacher

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 7, 2005-2032

Abstract: We consider time series with a seasonal component that varies randomly in length and shape. The shape parameters of the seasonal process, as well as the noise component, are stationary and exhibit long-range dependence. A functional limit theorem for the estimated parameter process leads to asymptotic inference under suitable conditions on the observational grid. The model is motivated by a study of the effect of body positioning on respiratory muscles during weaning (Walterspacher et al. 2017).

Date: 2025
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DOI: 10.1080/03610926.2024.2355582

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