COVARIANCE-BASED ORTHOGONALITY TESTS FOR REGRESSORS WITH UNKNOWN PERSISTENCE
提出一种基于协方差零约束的正交性新检验，适用于预测变量接近单位根的情形，避免标准回归检验的尺寸扭曲，且不要求因变量与预测变量同阶单整，能检测更丰富的备择假设。
This paper develops a new test of orthogonality based on a zero restriction on the covariance between the dependent variable and the predictor. The test provides a useful alternative to regression-based tests when conditioning variables have roots close or equal to unity. In this case standard predictive regression tests can suffer from well-documented size distortion. Moreover, under the alternative hypothesis, they force the dependent variable to share the same order of integration as the predictor, whereas in practice the dependent variable often appears stationary and the predictor may be near-nonstationary. By contrast, the new test does not enforce the same orders of integration and is therefore capable of detecting a rich set of alternatives to orthogonality that are excluded by the standard predictive regression model. Moreover, the test statistic has a standard normal limit distribution for both unit root and local-to-unity conditioning variables, without prior knowledge of the local-to-unity parameter. If the conditioning variable is stationary, the test remains conservative and consistent. Simulations suggest good small-sample performance. As an empirical application, we test for the predictability of stock returns using two persistent predictors, the dividend-price ratio and short-term interest rate.