A Simple Test for Spurious Regressions-假回归的简单检验

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英文文献：A Simple Test for Spurious Regressions-假回归的简单检验
英文文献作者：Antonio E. Noriega,Daniel Ventosa-Santaularia
英文文献摘要：
The literature on spurious regressions has found that the t-statistic for testing the null of no relationship between two independent variables diverges asymptotically under a wide variety of nonstationary data generating processes for the dependent and explanatory variables. This paper introduces a simple method which guarantees convergence of this t-statistic to a pivotal limit distribution, when there are drifts in the integrated processes generating the data, thus allowing asymptotic inference. We show that this method can be used to distinguish a genuine relationship from a spurious one among integrated (I(1) and I(2)) processes. Simulation experiments show that the test has good size and power properties in small samples. We apply the proposed procedure to several pairs of apparently independent integrated variables (including the marriages and mortality data of Yule, 1926), and find that our procedure, in contrast to standard ordinary least squares regression, does not find (spurious) significant relationships between the variables.

关于伪回归的文献发现，检验两个自变量之间无关系的零相关性的t统计量在依赖变量和解释变量的各种非平稳数据生成过程下渐近发散。本文介绍了一种简单的方法，当生成数据的集成过程存在漂移时，该方法保证t统计量收敛到一个关键的极限分布，从而允许渐近推理。我们证明了该方法可以用来区分集成(I(1)和I(2))过程之间的真实关系和虚假关系。仿真实验表明，该测试在小样本中具有良好的尺寸和功率特性。我们将所提出的程序应用于几对明显独立的整合变量(包括1926年的Yule的婚姻和死亡数据)，并发现，与标准的普通最小二乘回归相比，我们的程序没有发现变量之间的显著关系(虚假的)。

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