Testing the predictability of the predictive regression model is of great interest in economics and finance. Recently, (Zhu et al. (2014) Predictive regressions for macroeconomic data, Vol. 8, pp. 577–594.) proposed a unified test to account for this issue. Their test has a desirable property that its limit distribution is standard regardless of the regressor being stationary, near unit root or unit root. However, this test depends on, a priori, whether there is an intercept in the predictive regression while this is usually unknown in practice. In this paper, using empirical likelihood inference, we develop a unified pretest for the intercept, as a pretest to determine the choice of the predictability test. Simulations studies confirm that the proposed pretest works well. Two real data examples are also provided to illustrate the importance of such pretest. The first revisits the S&P 500 index data and the second investigates stock return predictability and investor sentiment for six countries.

中文翻译：

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预测回归模型截距的统一测试*

测试预测回归模型的可预测性在经济学和金融学中引起了极大的兴趣。最近，（Zhu等人（2014年），《宏观经济数据的预测回归》，第8卷，第577-594页。）提出了统一的检验方法来解决这个问题。他们的测试具有令人满意的特性，即无论回归变量是静止的，接近单位根还是单位根，其极限分布都是标准的。但是，此测试取决于先验，预测回归中是否存在截距，而这在实践中通常是未知的。在本文中，使用经验似然推断，我们为截距开发了统一的预测试，作为确定可预测性测试选择的预测试。仿真研究证实，提出的预测试效果很好。还提供了两个真实的数据示例来说明这种预测试的重要性。前者回顾了标准普尔500指数数据，而后者则考察了六个国家的股票回报可预测性和投资者情绪。