This article argues that there are several logical reasons for the existence of asymmetric causal effects that need to be taken into account but usually are neglected in the literature. It suggests allowing for asymmetry in the causality testing by using the cumulative sums of positive and negative shocks. A bootstrap simulation approach with leverage adjustment is used to generate critical values that are robust to non-normality and time-varying volatility. An application to the efficient market hypothesis in the UAE is provided. The results show that the equity market is informationally efficient with regard to the oil shocks regardless if these shocks are positive or negative.