Forecast Accuracy after Pretesting with an Application to the Stock Market

In econometrics, as a rule, the same data set is used to select the model and, conditional on the selected model, to forecast.However, one typically reports the properties of the (conditional) forecast, ignoring the fact that its properties are affected by the model selection (pretesting).This is wrong, and in this paper we show that the error can be very substantial.We obtain explicit expressions for this error.To illustrate the theory we consider the regression approach of Pesaran and Timmermann (1994) to stock market forecasting, and show that their proposed recursive predictions are much less robust than naive econometrics might suggest.