Yule-Walker-Based Approaches for Estimation of Noise-Corrupted Periodic Autoregressive Model - Finite- and Infinite-Variance Cases

Periodic autoregressive (PAR) time series with finite variance is considered one of the most known second-order cyclostationary models. However, in the real applications, the signals with the periodic structure very often are disturbed by additional noise (called additive noise, AN) that may be related to measurement device disturbances or other external sources. Thus, the known estimation techniques dedicated to pure PAR models may be inefficient for such cases. In this paper, the problem of parameters estimation for PAR models with AN is considered. Several known Yule-Walker-based methods dedicated to noise-corrupted PAR time series are discussed and compared using Monte Carlo simulations. The efficiency of all methods is verified for selected distributions of AN. Most of all, we consider the model with infinite-variance (alpha-stable) additive noise, which was not analyzed in the literature before. For such a model, a novel estimation method based on fractional lower-order covariance and high-order Yule-Walker equations is proposed.