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.

翻译：暂无翻译