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.

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To cite this article: Chunhao Cai & Yiwu Shang (05 Aug 2025): Parameter estimation for fractional autoregressive process with seasonal structure, Statistical Theory and Related Fields, DOI: 10.1080/24754269.2025.2537487

To link to this article: https://doi.org/10.1080/24754269.2025.2537487