This paper introduces a new periodic fractional autoregressive process (PFAR) driven by fractional Gaussian noise (fGn) to model time series of precipitation evapotranspiration. Compared with the similar model in [\emph{Water Resources Research}, \textbf{20} (1984) 1898--1908], the new model incorporates a periodic structure via specialized varying coefficients and captures long memory and rough voltality through fGn for $0<H<1$, rather than via fractional differencing. In this work, Generalized Least Squares Estimation (GLSE) and the GPH method are employed to construct an initial estimator for the joint estimation of model parameters. A One-Step procedure is then used to obtain a more asymptotically efficient estimator. The paper proves that both estimators are consistent and asymptotically normal, and their performance is demonstrated via Monte Carlo simulations with finite-size samples. Simulation studies suggest that, while both estimation methods can accurately estimate the model parameters, 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，用于模拟降水蒸散时间序列。与《水资源研究》1984年第20卷第1898-1908页中的类似模型相比，新模型通过特定的时变系数引入周期性结构，并利用分数高斯噪声捕捉长记忆性和粗糙波动性，而非通过分数差分实现。本研究采用广义最小二乘估计和GPH方法构建模型参数的联合初始估计量，随后通过一步法获得渐近效率更高的估计量。论文证明了两种估计量均具有一致性和渐近正态性，并通过有限样本的蒙特卡洛模拟验证了其性能。模拟研究表明，虽然两种估计方法均能准确估计模型参数，但一步法估计量的性能优于初始估计量。