Statistical model selection criteria provide an informed choice of the model with best external (i.e., out-of-sample) validity. Therefore they guard against overfitting ("data snooping"). We implement several model selection criteria in order to verify recent evidence of predictability in excess stock returns and to determine which variables are valuable predictors. We confirm the presence of in-sample predictability in an international stock market dataset, but discover that even the best prediction models have no out-of-sample forecasting power. The failure to detect out-of-sample predictability is not due to lack of power.