Return Predictability Under the Alternative

Long-horizon predictability is not a myth. We propose a new analytical standard error for predictive regressions that does not impose the null hypothesis that returns are unpredictable and exhibits substantial power gains relative to popular tests. Deriving the covariance matrix under the alternative hypothesis produces two new terms capturing the volatility of shocks to the regressor and their correlation with shocks to the prediction equation. Empirically, we show that failure to detect long-horizon predictability comes from lower power in tests derived under the null hypothesis. For many predictors, giving the alternative a chance allows short-run predictability to survive at long-horizons.