This paper introduces a new kind of periodic fractional autoregressive process (PFAR) driven by fractional Gaussian noise (fGn). The new model is a specialized varying coefficient fractional autoregressive model, where the coefficients adhere to a periodic structure. In this working, Generalized least squares estimation and GPH method are employed to construct an initial estimator to estimate the joint estimation of the parameters of these models. Then one-step procedure is used to obtain a more asymptotically-efficient estimator. The paper proves that both estimators are consistent and asymptotically normal, and their performance is demonstrated through a simulation study using finite-size samples via Monte Carlo simulations. Simulation studies suggests that, while both estimation methods can accurately estimate the model, the one-step estimator outperforms the initial estimator.

翻译：本文提出了一种由分数高斯噪声驱动的周期性分数自回归过程。该新模型是一种特殊的变系数分数自回归模型，其系数遵循周期结构。本研究采用广义最小二乘估计与GPH方法构建初始估计量，以估计这些模型的联合参数。随后，通过一步法获得具有更高渐近效率的估计量。本文证明了两种估计量均具有一致性与渐近正态性，并通过基于有限样本的蒙特卡洛模拟研究验证了其性能。模拟研究表明，尽管两种估计方法均能准确估计模型，但一步估计量的表现优于初始估计量。