An information criterion for detecting periodicities in functional time series

An information criterion is proposed for determining the unknown number of periodic components in functional time series. Identifying the number of frequencies in large-scale time series has been a central problem. An iterative procedure is introduced based on the residual process obtained via least squares fitting, which exhibits broad applicability. The consistency of the estimated number of periodic components is established through minimization of the information criterion. The efficacy of the procedure is illustrated through numerical simulations. In real data analysis, the proposed method is applied to temperature data and sunspot data.