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

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. Citation2017).