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.

翻译：本研究探讨预测回归中系数随机性的检验问题，重点分析系数随机性检验如何受随机系数持久性的影响。研究发现：当随机系数为平稳过程（即I(0)）时，Nyblom（1989）提出的LM检验在功效方面失去其最优性——该最优性原本是针对积分过程（即I(1)）随机系数的备择假设建立的。我们通过构造检验方法证明，在随机系数平稳的情形下，这些方法比LM检验具有更高功效，尽管当随机系数为积分过程时其功效低于LM检验。这表明系数随机性的最优检验方法因情境而异，实践者需根据潜在随机系数的持久性从多种检验中择优选择。特别地，通过理论推导与数值模拟，我们证明：当缺乏潜在随机系数持久性的先验信息时，采用LM检验与本文提出的Wald型检验的乘积形式更为理想。这一结论通过美国股票收益数据的实证分析得以验证。