Large Sample Properties of Parameter Estimates for Periodic ARMA Models

This paper studies the asymptotic properties of parameter estimates for causal and invertible periodic autoregressive moving‐average (PARMA) time series models. A general limit result for PARMA parameter estimates with a moving‐average component is derived. The paper presents examples that explicitly identify the limiting covariance matrix for parameter estimates from a general periodic autoregression (PAR), a first‐order periodic moving average (PMA(1)), and the mixed PARMA(1,1) model. Some comparisons and contrasts to univariate and vector autoregressive moving‐average sequences are made.