Transformed regression-based long-horizon predictability tests

We propose new tests for long-horizon predictability based on IVX estimation of a transformed regression which explicitly accounts for the over-lapping nature of the dependent variable in the long-horizon regression arising from temporal aggregation. To improve efficiency, we moreover incorporate the residual augmentation approach recently used in the context of short-horizon predictability testing by Demetrescu and Rodrigues (2022). Our proposed tests improve on extant tests in the literature in a number of ways. First, they allow practitioners to remain ambivalent over the strength of the persistence of the predictors. Second, they are valid under much weaker conditions on the innovations than extant long-horizon predictability tests; in particular, we allow for general forms of conditional and unconditional heteroskedasticity in the innovations, neither of which are tied to a parametric model. Third, unlike the popular Bonferroni-based methods in the literature, our proposed tests can handle multiple predictors, and can be easily implemented as either one or two-sided hypotheses tests. Monte Carlo analysis suggests that our preferred tests offer improved finite sample properties compared to the leading tests in the literature. We report results from an empirical application investigating the use of real exchange rates for predicting nominal exchange rates and inflation.