Inference of Long-Horizon Predictability

Examination over multiple horizons has been a routine in testing asset return predictability in finance and macroeconomics. In a simple predictive regression model, we find that the popular scaled test for multiple-horizon predictability has zero null rejection rate if the forecast horizon increases at a faster rate than the inverse of proximity of the predictor autoregressive root to the unity. Correspondingly, the scaled test has zero power for long horizons, e.g. if the horizon increases faster than n1/2, where n is the sample size, when the predictor is stationary. The t-test based on an implication of the short-run model, together with Bonferroni correction we suggest, is shown to have controlled size agnostic of persistence of the predictor, and is uniformly more powerful than the robust scaled test. Simulation experiments support the asymptotic results and show substantial power gain of the implied test over various other tests. In the empirical application, we re-examine predictive ability of the short interest and the dividend-price-ratio for aggregate equity premium.