Forecasting with Misspecified Models

S ummary In this paper we examine the situation where, for a single time series, an incorrect model is assumed. The cost of this misspecification, in terms of increased expected‐squared‐error of prediction, is derived. The case where the assumed model is autoregressive is examined in detail with estimation error taken into account. Our main conclusions are that, for sample sizes that often occur in practice, fitted autoregressive models of high order can yield grossly sub‐optimal forecasts.