Finite Sample Prediction and Overdifferencing

If the process generating a time series contains a deterministic component the differencing operations carried out to achieve stationarity may lead to an ARMA model which is strictly noninvertible. This is known as overdifferencing but it is shown here that overdifferencing need not have serious implications for prediction provided that a finite sample prediction procedure is used. The proposed method is based on the Kalman filter and it allows both the optimal predictors and their mean square errors to be computed.