Understanding Equation Balance in Time Series Regression
Understanding Equation Balance in Time Series Regression
复制标题
了解时间序列回归中的方程平衡
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Christopher Wlezien
中科院分区：
文献类型：
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作者：
P. Enns;Christopher Wlezien
政治分析（PA）最近举办了一个关于时间序列分析的研讨会，该研讨会建立在De Boef和Keele（2008）在美国政治学杂志上发表的有影响力的时间序列文章的基础上。方程平衡是整个研讨会的一个重点。Banerjee等人（1993，164）在他们关于这个问题的经典著作中解释说，不平衡方程是一个回归方程，“其中回归和不是与回归量相同的积分顺序，或者回归量的任何线性组合。这次研讨会的贡献者强调方程平衡的重要性是正确的，因为不平衡的方程可以产生序列相关的残差（例如，Pagan and Wickens 1989）和虚假关系（例如，Banerjee等人，1993，79）。然而，在整个PA研讨会上，方程平衡以不同的方式定义和应用。Grant和乐博（2016，7）遵循Banerjee等人的观点。的定义，当他们解释说，一般误差修正模型（GECM）-或自回归分布滞后（ADL）-是平衡的，如果协整存在。Keele、Linn和Webb（2016 a，第83页）在讨论方程平衡时引用了Bannerjee et al.（1993）的话，在他们对研讨会的第二篇贡献中含蓄地表达了同样的观点。然而，研讨会的其他部分似乎应用了更严格的方程平衡标准，指出在估计GECM/ADL时，所有时间序列必须是相同的积分阶数。正如格兰特和乐博在他们的第一篇文章的摘要中所写的那样，“各种积分阶数的时间序列--平稳的、非平稳的、爆炸的、近似的和分数积分的--不应该放在一起分析。. .也就是说，没有方程平衡，模型是错误的，假设检验和长期乘数是不可靠的。Keele，Linn和Webb（2016 b，34）也同样写道：“当整合的顺序混合时，没有回归模型是合适的，因为当方程不平衡时，不存在长期关系。Box-Steffensmeier和Helgason（2016，2）指出了这一点，“当研究两个（或更多）系列之间的关系时，分析师必须确保它们具有相同的集成水平;也就是说，它们必须是平衡的。”虽然Freeman（2016）对方程平衡提供了一个更微妙的观点，但许多研讨会的贡献者可以被解释为建议学者永远不要混合积分顺序。事实上，乐博和格兰特在他们的总结文章中写道：“这些论文的一个共识是，方程平衡是一个重要但被忽视的话题。在GECM或ADL中，不能将平稳变量、单位根变量和分数积分变量混合在一起。
Political Analysis (PA) recently hosted a symposium on time series analysis that built upon De Boef and Keele’s (2008) influential time series article in the American Journal of Political Science. Equation balance was an important point of emphasis throughout the symposium. In their classic work on the subject, Banerjee et al. (1993, 164) explain that an unbalanced equation is a regression, “in which the regressand is not the same order of integration as the regressors, or any linear combination of the regressors.” The contributors to this symposium were right to emphasize the importance of equation balance, as unbalanced equations can produce serially correlated residuals (e.g., Pagan and Wickens 1989) and spurious relationships (e.g., Banerjee et al. 1993, 79). Throughout the PA symposium, however, equation balance is defined and applied in different ways. Grant and Lebo (2016, 7) follow Banerjee et al.’s definition when they explain that a general error correction model (GECM)— or autoregressive distributed lag (ADL)—is balanced if cointegration is present. Keele, Linn and Webb (2016a, 83) implicitly make this same point in their second contribution to the symposium when they cite Bannerjee et al. (1993) in their discussion of equation balance. Yet, other parts of the symposium seem to apply a stricter standard of equation balance, stating that when estimating a GECM/ADL all time series must be the same order of integration. As Grant and Lebo write in the abstract of their first article, “Time series of various orders of integration— stationary, non-stationary, explosive, nearand fractionally integrated—should not be analyzed together . . . That is, without equation balance the model is misspecified and hypothesis tests and long-run-multipliers are unreliable.” Keele, Linn and Webb (2016b, 34) similarly write, “no regression model is appropriate when the orders of integration are mixed because no long-run relationship can exist when the equation is unbalanced.” Box-Steffensmeier and Helgason (2016, 2) make the point by stating, “when studying the relationship between two (or more) series, the analyst must ensure that they are of the same level of integration; that is, they have to be balanced.” Although Freeman (2016) offers a more nuanced perspective on equation balance, many of the symposium contributors could be interpreted as recommending that scholars never mix orders of integration. Indeed, in their concluding article, Lebo and Grant write, “One point of agreement among the papers here is that equation balance is an important and neglected topic. One cannot mix together stationary, unit-root, and fractionally integrated variables in either the GECM or the ADL” (p.79).