2025/03/29 by Chunhao Cai, Cai, Chunhao, Shang, Yiwu
Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2503.23089
openalex publication_date 2025/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.