Periodic autoregressive (PAR) time series is considered as one of the most common models of second-order cyclostationary processes. In real applications, the signals with periodic characteristics may be disturbed by additional noise related to measurement device disturbances or to other external sources. The known estimation techniques for PAR models assume noise-free model, thus may be inefficient for such cases. In this paper, we propose four estimation techniques for the noise-corrupted finite-variance PAR models. The methodology is based on Yule-Walker equations utilizing the autocovariance function. Thus, it can be used for any type of the finite-variance additive noise. The presented simulation study clearly indicates the efficiency of the proposed techniques, also for extreme case, when the additive noise is a sum of the Gaussian additive noise and additive outliers. This situation corresponds to the real applications related to condition monitoring area which is a main motivation for the presented research.

翻译：周期自回归（PAR）时间序列被视为二阶循环平稳过程的最常见模型之一。在实际应用中，具有周期特征的信号可能受到与测量设备干扰或其他外部源相关的附加噪声干扰。已知的PAR模型估计技术假设模型无噪声，因此在此类情况下可能效率低下。本文针对受噪声污染的有限方差PAR模型提出了四种估计技术。该方法基于利用自协方差函数的Yule-Walker方程，因此可适用于任意类型的有限方差加性噪声。仿真研究表明，即使在极端情况下——加性噪声为高斯加性噪声与加性离群值的叠加，所提技术仍具有效性。该情形对应于状态监测领域的实际应用，这也是本研究的核心动机。