论文标题：Is Stock Price Correlated with Oil Price? Spurious Regressions with Moderately Explosive Processes.

　　发表时间：2019

　　论文所有作者：Ye CHEN and Yundong Tu

　　期刊名及所属分类：Oxford Bulletin of Economics and Statistics(国际B)

　　英文摘要：This study explores the spurious effects in linear regressions with moderately explosive processes. Asymptotic results are developed for the least square estimator, the typical t ‐statistic, the Durbin–Watson statistic, and the coefficient of determination. The typical t ‐statistic is unable to detect the presence of a spurious relationship, due to the presence of nuisance parameters that characterize deviations from unity. Moreover, the t ‐statistic for common explosive processes has different asymptotics compared to that for distinct explosive processes. Such differences further complicate the use of the t ‐statistic. We demonstrate that two popular methods available in the literature are incapable for this purpose due to similar difficulties. To overcome these limitations, we propose a t ‐test based upon balanced regressions that induces asymptotic inference based on the standard normal distribution, which is therefore robust to deviations from unity. These results are further generalized to spurious regressions with multivariate mildly explosive processes. Simulation results confirm that our test is effective in finite samples, while other alternatives are not. An empirical example that demonstrates the phenomenon of spurious correlation between the NASDAQ stock index and crude oil price in the US is provided to show the practical merit of our proposed method.

　　中文摘要：本研究探讨了中等爆炸过程线性回归中的虚假效应。给出了最小二乘估计、典型t统计量、Durbin-Watson统计量和决定系数的渐近结果。典型的t统计无法检测到虚假关系的存在，这是由于存在表征偏离统一的有害参数。此外，与不同的爆炸过程相比，普通爆炸过程的t统计量具有不同的渐近性。这种差异使t统计量的使用更加复杂。我们证明，两种流行的方法可用的文献是不能为这一目的由于相似的困难。为了克服这些限制，我们提出了一种基于平衡回归的t检验，该t检验引入了基于标准正态分布的渐近推断，因此对偏离统一的情况具有鲁棒性。这些结果进一步推广到多变量轻度爆炸过程的伪回归。仿真结果表明，我们的方法在有限样本下是有效的，而其他方法则是无效的。通过对美国纳斯达克指数与原油价格伪相关现象的实证分析，证明了本文方法的实用性。