Artificial Skill due to Predictor Screening

Abstract

This paper shows that if predictors are selected preferentially because of their strong correlation with a prediction variable, then standard methods for validating prediction models derived from these predictors will be biased. This bias is demonstrated by screening random numbers and showing that regression models derived from these random numbers have apparent skill, in a cross-validation sense, even though the predictors cannot possibly have the slightest predictive usefulness. This result seemingly implies that random numbers can give useful predictions, since the sample being predicted is separate from the sample used to estimate the regression model. The resolution of this paradox is that, prior to cross validation, all of the data had been used to evaluate correlations for selecting predictors. This situation differs from real-time forecasts in that the future sample is not available for screening. These results clarify the fallacy in assuming that if a model performs well in cross-validation mode, then it will perform well in real-time forecasts. This bias appears to afflict several forecast schemes that have been proposed in the literature, including operational forecasts of Indian monsoon rainfall and number of Atlantic hurricanes. The cross-validated skill of these models probably would not be distinguishable from that of a no-skill model if prior screening were taken into account.