The Bias of Forecasts from a First-Order Autoregression

The exact finite sample behavior is investigated on the bias of multiperiod leastsquares forecasts in the normal autoregressive model <italic>y</italic><italic>null</italic> = α + β<italic>y</italic>_null + <italic>u</italic><italic>null</italic>. Necessary and sufficient conditions are given for the existence of the bias and an expression is presented which we use to obtain exact numerical results for finite samples. The unit root and near unit root behavior is studied in detail and some popular preconceptions about the behavior of the bias are shown to be false.