Robust tests of stock return predictability under heavy-tailed innovations

This paper provides a robust test of predictability under the predictive regression model with possible heavy-tailed innovations assumption, in which the predictive variable is persistent and its innovations are highly correlated with returns. To this end, we propose a robust test which can capture empirical phenomena such as heavy tails, stationary, and local to unity. Moreover, we develop related asymptotic results without the second-moment assumption between the predictive variable and returns. To make the proposed test reasonable, we propose a generalized correlation and provide theoretical support. To illustrate the applicability of the test, we perform a simulation study for the impact of heavy-tailed innovations on predictability,as well as direct and/or indirect implementation of heavy-tailed innovations to predictability via the unit root phenomenon. Finally, we provide an empirical study for further illustration,to which the proposed test is applied to a U.S. equity data set.