Parameter estimation for fractional autoregressive process with seasonal structure

• Published in: Statistical theory and related fields pp. 1 - 30
• Main Authors: Cai, Chunhao, Shang, Yiwu
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 05.08.2025
• Subjects: fractional Gaussian noise; one-step procedure; Seasonal autoregressive process
• ISSN: 2475-4269; 2475-4277
• DOI: 10.1080/24754269.2025.2537487

This paper introduces a new kind of seasonal fractional autoregressive process (SFAR) driven by fractional Gaussian noise (fGn). The new model includes a standard seasonal AR model and fGn. The estimation of the parameters of this new model has to solve two problems: nonstationarity from the seasonal structure and long memory from fGn. We innovatively solve these by getting a stationary subsequence, making a stationary additive sequence and then obtaining their spectral density. Then we use one-step procedure for Generalized Least Squares Estimator (GLSE) and the Geweke Porter–Hudak (GPH) method to get better results. We prove that both the initial and one-step estimators are consistent and asymptotically normal. Finally, we use Monte Carlo simulations with finite-sized samples to demonstrate the performance of these estimators. Moreover, through empirical analysis, it is shown that the SFAR model can simulate some real-world phenomena better than general models.