Seasonal Periodic Autoregressive Processes with Values in Hilbert Spaces

Abstract

Time series analysis is a widely used technique in data analytics.This paper introduces a new model, the first-order seasonalperiodic autoregressive Hilbertian process, designed for functional timeseries analysis. This model integrates elements of both first-order periodicautoregressive Hilbertian and seasonal Hilbertian autoregressivemodels. The paper outlines key properties of this process, including itsauto-covariance operators, and discusses its alignment with the law oflarge numbers and the central limit theorem.