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).
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