Transformed Regression-based Long-Horizon Predictability Tests

We propose new tests for long-horizon predictability based on IVX estimation (see Kostakis et al., 2015) of transformed regressions. These explicitly account for the over-lapping nature of the dependent variable which features in a long-horizon predictive regression arising from temporal aggregation. Because we use IVX estimation we can also incorporate the residual augmentation approach recently used in the context of short-horizon predictability testing by Demetrescu and Rodrigues (2020) to improve efficiency. Our proposed tests have a number of advantages for practical use. First, they are simple to compute making them more appealing for empirical work than, in particular, the Bonferroni-based methods developed in, among others, Valkanov (2003) and Hjalmarsson (2011), which require the computation of confidence intervals for the autoregressive parameter characterising the predictor. Second, unlike some of the available tests, they allow the practitioner to remain ambivalent as to whether the predictor is strongly or weakly persistent. Third, the tests are valid under considerably weaker assumptions on the innovations than extant long-horizon predictability tests. In particular, we allow for quite general forms of conditional and unconditional heteroskedasticity in the innovations, neither of which are tied to a parametric model. Fourth, our proposed tests can be easily implemented as either one or two-sided hypotheses tests, unlike the Bonferroni-based methods which require the computation of different confidence intervals for the autoregressive parameter depending on whether left or right tailed tests are to be conducted (see Hjalmarsson, 2011). Finally our approach is straightforwardly generalisable to a multi-predictor context. Monte Carlo analysis suggests that our preferred test displays improved finite properties compared to the leading tests available in the literature. We also report an empirical application of the methods we develop to investigate the potential predictive power of real exchange rates for predicting nominal exchange rates and inflation.