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. We apply tests for coefficient constancy to real data. The results mostly reverse the conclusion of an earlier empirical study.

翻译：本研究探讨了预测回归中系数随机性的检验问题。我们重点关注系数随机性检验如何受到随机系数持久性的影响。研究发现，当随机系数为平稳（即I(0)）时，Nyblom（1989）提出的LM检验会丧失其最优性（从检验功效角度而言），因为该检验原本是针对积分（即I(1)）随机系数的备择假设而建立的。为此，我们构建了在随机系数平稳时比LM检验更具功效的检验方法——尽管当随机系数为积分过程时，这些检验在检验功效上不及LM检验。这表明系数随机性的最优检验方法因具体情况而异，实践者需根据潜在随机系数的持久性特征，从多种检验中做出相应选择。我们将系数恒定性检验应用于真实数据，所得结果基本推翻了此前一项实证研究的结论。