Taking stock of long-horizon predictability tests: Are factor returns predictable?

Abstract

This study provides a critical assessment of long-horizon return predictability tests using highly persistent regressors. We show that the commonly used statistics are typically oversized, leading to spurious inference. Instead, we propose a Wald statistic, which accommodates multiple predictors of (unknown) arbitrary persistence degree within the I(0)-I(1) range. The test statistic, based on an adaptation of the IVX procedure to a long-horizon regression framework, is shown to have a standard chi-squared asymptotic distribution (regardless of the stochastic properties of the regressors used as predictors) and to exhibit excellent finite-sample size and power properties. Employing this test statistic, we find evidence of predictability for “old” and “new” pricing factors with monthly returns, but this becomes weaker as the predictive horizon increases. The predictability evidence substantially weakens with annual data. Overall, we question the incremental value of using long-horizon predictive regressions.