Estimation of coefficients for periodic autoregressive model with additive noise -- a finite-variance case

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.