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arXiv · 2503.23089

Parameter estimation for fractional autoregressive process with seasonal structure

Chunhao Cai·Yiwu Shang
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Abstract

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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Chunhao Cai, Yiwu Shang. 2025-03-29. Parameter estimation for fractional autoregressive process with seasonal structure. https://arxiv.org/abs/2503.23089

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