基于自相关视角的弱平稳过程之间的伪回归分析

The Analysis of Spurious Regressions Between Weak Stationary Processes Based on Autocorrelation Perspective

随机干扰项之间的未知形式自相关是导致相互独立的弱平稳过程之间伪回归的主要原因。通过理论分析和一系列的蒙特卡罗模拟,揭示了数据过程本身的持久性、样本容量T和随机干扰项自相关之间的内在联系。研究发现随机干扰项往往呈现出与数据过程阶数相同的自相关。进一步研究表明,运用广义差分法和Cochrane-Orcutt迭代法虽然能大大减少伪回归概率,但在有些情况下,即使当样本容量较大时,较高阶的Cochrane-Orcutt迭代法仍然无法避免伪回归的发生。

The reason behind the spurious regressions between weak stationary processes is unknown form autocorrelation of random terms.The paper reveals the inherent relationship among the persistence of data processes,sample size and the autocorrelation of random terms through a series of Monte Carlo simulations.The study finds that random term shows the same order autocorrelation with the autocorrelation of data processes.Further study shows that generalized difference method and Cochrane-Orcutt iterative method can greatly reduce the probability of spurious regressions between stationary processes.But in some cases,even when the sample size is larger,higher-order Cochrane-Orcutt iterative method still can not avoid the occurrence of spurious regressions.