Estimating SPARMA Models with Dependent Error Terms

We are interested in a class of seasonal autoregressive moving average (SARMA) models with periodically varying parameters, so-called seasonal periodic autoregressive moving average (SPARMA) models under the assumption that the errors are uncorrelated but non-independent (i.e. weak SPARMA models). Relaxing the classical independence assumption on the errors considerably extends the range of application of the SPARMA models, and allows one to cover linear representations of general nonlinear processes. We establish the asymptotic properties of the quasi-generalized least squares (QLS) estimator of these models. Particular attention is given to the estimation of the asymptotic variance matrix of the QLS estimator, which may be very different from that obtained in the standard framework. A set of Monte Carlo experiments are presented.