Testing for Stationary or Persistent Coefficient Randomness in Predictive Regressions

This study considers tests for coefficient randomness in predictive regressions. Our focus is on how tests for coefficient randomness are influenced by the persistence of random coefficient. We find 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 tests that are more powerful than the LM test when random coefficient is stationary, although these tests are dominated in terms of power by the LM test when random coefficient is integrated. This implies that the best test for coefficient randomness differs from context to context, and practitioners should take into account the persistence of potentially random coefficient and choose from several tests accordingly. In particular, we show through theoretical and numerical investigations that the product of the LM test and a Wald-type test proposed in this paper is preferable when there is no prior information on the persistence of potentially random coefficient. This point is illustrated by an empirical application using the U.S. stock returns data.