Predictability Hidden by Anomalous Observations∗

Predictive relations motivated by financial theory should hold at least for the majority of the data, but they can be violated by a small fraction of the data. Conventional testing approaches can fail to detect predictive relations that hold for the vast majority of the data, because rare anomalous observations can have an excessive influence on the results. We propose a novel robust method for testing the null of no predictability, using predictive regression models that might be violated by a minority of anomalous observations. The Monte Carlo evidence demonstrates large improvements of our approach, while the empirical analysis produces a sharp evidence of market return predictability – using predictive variables like the dividend yield, the volatility risk premium, or labor income – which is valid for the vast majority of the data.