Kalman filter estimation for periodic autoregressive-moving average models

An exact maximum likelihood procedure is presented for estimating the parameters of a periodic autogressive-moving average (PARMA) model. To develop an estimator which is both statistically and computationally efficient, the PARMA class of models is written using a state-space representation and a Kalman filtering algorithm is used to estimate the parameters. In order to demonstrate how to fit PARMA models in practice, the most appropriate types of PARMA models are identified for fitting to two average monthly riverflow time series and the new estimator is employed for estimating the model parameters.