Predictive Regression and Robust Hypothesis Testing: Predictability Hidden by Anomalous Observations∗

Testing procedures for predictive regressions with lagged autoregressive variables imply a suboptimal inference in presence of small violations of ideal assumptions. We propose a novel testing framework resistant to such violations, which is consistent with nearly integrated regressors and applicable to multi-predictor settings, when the data may only approximately follow a predictive regression model. The Monte Carlo evidence demonstrates large improvements of our approach, while the empirical analysis produces a strong robust evidence of market return predictability, using predictive variables such as the dividend yield, the volatility risk premium or, labor income.