Estimation of ARMA Models with seasonal parameters

The Yule‐Walker equations for ARMA (p, q) models with periodic parameters are derived from which moment estimates can be obtained. Specifically, for the case of ARMA (p, 1) models, the periodic autoregressive parameters can be found by solving a system of linear equations, while the periodic moving average parameters satisfy a system of equations which can be solved iteratively. Particular examples are given and comparisons are made between the proposed moment estimates and estimates given previously.