Seasonal Periodic Autoregressive Processes with Values in Hilbert Spaces

Authors

  • Atefeh Zamani Department of Statistics Lecturer in Statistics School of Mathematics and Statistics, University of New South Wales Australia
  • Maryam Hashemi Statistics department, Khansar campus, University of Isfahan
  • Zahra Sajjadnia Department of Statistics Assistant Professor of Statistics Shiraz University Shiraz, Iran

DOI:

https://doi.org/10.30495/jme.v18i0.3188

Keywords:

First-order periodic autoregressive, Hilbertian process, Limiting properties, Multiplicative seasonal autoregressive.

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.

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Published

2025-02-19

Issue

Vol. 18

Section

Vol. 18, No. 11, (2024)

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