Testing for stationary or persistent coefficient randomness in predictive regressions

We consider tests for coefficient randomness in predictive regressions and study how they are influenced by the persistence of random coefficient. We show that when the random coefficient is stationary, or I(0), Nyblom’s (1989) LM test loses its optimality (in terms of power), which is established against the alternative of integrated, or I(1), random coefficient. We demonstrate this by constructing a test that is more powerful than the LM test when the random coefficient is stationary, although the test is dominated in terms of power by the LM test when the random coefficient is integrated. The power comparison is made under the sequence of local alternatives that approaches the null hypothesis at different rates depending on the persistence of the random coefficient and which test is considered. We revisit an earlier empirical research and apply the tests considered in this study to the U.S. stock returns data. The result mostly reverses the earlier finding. We also identify periods when predictability manifests.