趋势成分引起的虚假回归问题解决方法研究

本文研究了由序列中趋势成分引起的虚假回归问题的解决方法。发现在模型设定式中加入趋势变量，并考虑趋势存在结构突变的情况，再根据残差是否存在自相关进行可行广义最小二乘（FGLS）或普通最小二乘（OLS）估计，可以有效解决趋势成分引起的虚假回归问题。通过理论分析表明，采用本文中的估计方法，所得检验两序列是否为虚假相关的t统计量渐近服从标准正态分布或与标准正态非常接近的分布。Monte Carlo模拟证实了该方法的有效性。最后以Yule(1926)中两高度虚假相关的时间序列为例，佐证文中结论。

Solutions of Spurious Regressions with Trending Variables

This paper examines spurious regressions with trending variables. The results show that the problem of spurious regression disappears if the trend functions are included as additional regressors, considering the possible structural breaks at the same time. OLS or FGLS should be used depending on whether the error is uncorrelated or not. This method can help alleviate or eliminate the problem of spurious regressions with trending variables. Our approach has been justified theoretically, as the t statistic testing the spurious correlation converges weakly to either the standard normal distribution or a distribution that is very close to the standard normal distribution. In addition, the validity of the approach has been confirmed by Monte Carlo simulations. Moreover, the spurious connection between the two time series in Yule (1926) has been successfully removed by applying our method, which justifies our approach again.