Combining Tests of Predictive Ability Theory and Evidence for Chilean and Canadian Exchange Rates

In this paper we focus on combining out-of-sample test statistics of the Martingale Difference Hypothesis (MDH) to explore whether a new combined statistic may induce a test with higher asymptotic power. Asymptotic normality implies that more power can be achieved by finding the optimal weight in a combined t-ratio. Unfortunately, this optimal weight is degenerated under the null of no predictability. To overcome this problem we introduce a penalization function that attracts the optimal weight to the interior of the feasible combination set. The new optimal weight associated with the penalization problem is well defined under the null, ensuring asymptotic normality of the resulting combined test. We show, via simulations, that our proposed combined test displays important gains in power and good empirical size. In fact, the new test outperforms its single components displaying gains in power up to 45%. Finally, we illustrate our approach with an empirical application aimed at testing predictability of Chilean and Canadian exchange rate returns.