Forecasting with prediction intervals for periodic autoregressive moving average models


Correspondence to: Paul. L. Anderson, Department of Mathematics and Computer Science, Albion College, Albion MI 49224, USA


Periodic autoregressive moving average (PARMA) models are indicated for time series whose mean, variance and covariance function vary with the season. In this study, we develop and implement forecasting procedures for PARMA models. Forecasts are developed using the innovations algorithm, along with an idea of Ansley. A formula for the asymptotic error variance is provided, so that Gaussian prediction intervals can be computed. Finally, an application to monthly river flow forecasting is given, to illustrate the method.