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.本文聚焦预测回归中的系数随机性检验问题，探究随机系数的持续性对各类检验方法的影响。研究发现，当随机系数为平稳过程（即I(0)过程）时，针对单整（I(1)）随机系数备择假设构建的尼布卢姆（Nyblom，1989）拉格朗日乘数（LM）检验，其原有的检验功效最优性将不复存在。本文通过构造新检验方法验证了上述结论：当随机系数为平稳过程时，该新检验的检验功效优于LM检验；而当随机系数为单整过程时，LM检验的功效则更为出色。本次功效比较基于局部备择假设序列展开，此类备择假设向原假设收敛的速率取决于随机系数的持续性以及所采用的具体检验方法。此外，本文重新审视了一项既往实证研究，将本文所提出的检验方法应用于美国股票收益率数据，所得结论与此前的研究发现基本相悖，并识别出了股票收益率呈现可预测性的时段。