New estimation method for periodic autoregressive time series of order 1 with additive noise

Abstract The periodic behavior of real data can be manifested in the time series or its characteristics. One characteristics that often manifests is sample autocovariance function. In this case, periodically correlated (PC) considered. main models exhibits PC property autoregressive (PARMA) model considered as generalization classical moving average (ARMA) process. However, when one considers data, practically observed trajectory corresponds to “pure” with additional noise which a result measurement device other external forces. Thus, paper we consider sum (PAR) and additive finite-variance distribution. We present properties indicating property. goals introduce new estimation method for model’s parameters. novel algorithm takes under consideration modification Yule–Walker utilizes Here, propose two versions method, namely robust ones. effectiveness proposed methodology verified by Monte Carlo simulations. comparison presented. approach universal applied any noise.