Testing for Stationary or Persistent Coefficient Randomness in Predictive Regressions

TL;DR

This paper develops and compares tests for coefficient randomness in predictive regressions, focusing on how their power varies with the persistence of the random coefficient, and revisits empirical results on U.S. stock returns.

Contribution

It introduces a new test more powerful for stationary coefficients and analyzes the impact of coefficient persistence on test performance.

Findings

New test outperforms LM test for stationary coefficients

LM test remains more powerful for integrated coefficients

Revised empirical conclusions on U.S. stock returns

Abstract

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 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.