Why Long Horizons: A Study of Power Against Persistent Alternatives

This paper studies tests of predictability in regressions with a given AR(1) regressor and an asset return dependent variable measured over a short or long horizon. The paper shows that when there is a persistent predictable component in the return, an increase in the horizon may increase the R2 statistic of the regression and the approximate slope of a predictability test. Mone Carlo experiments show that long-horizon regression tests have serious size distortions when asymptotic critical values are used, but some versions of such tests have power advantages remaining after size is corrected.