Testing Causality between Two Vectors in Multivariate Autoregressive Moving Average Models
多元ARMA模型中两个变量向量之间的因果性检验AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究经济时间序列中的多元ARMA与Granger非因果性检验。
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多元ARMA模型中两个变量向量之间的因果性检验
- 研究问题
- 在一般多元ARMA模型中，如何定义并检验两个变量向量间的Granger非因果性，尤其在向量未涵盖全部变量或存在奇异点时？
- 方法与思路
- 作者推导线性可逆过程及平稳可逆ARMA过程的非因果充要条件，讨论检验，并以序贯界限检验处理常规渐近条件失效的情形。
- 材料陈述的贡献
- 摘要称，论文建立向量间非因果条件与检验方法；加拿大货币和收入应用中，三变量模型给出不同于双变量模型的单向预测关系证据。
- 阅读关注点
- 应核对信息集合与可逆性设定、非因果条件的参数表达、奇异点处理，以及增加变量为何改变货币与收入的Granger关系判断。
- 阅读边界
- 仅据OpenAlex索引摘要，稿件版本未注明。Granger因果性关乎给定信息集下的预测关系；摘要未提供结构因果识别、具体检验数值或完整条件。
原文摘要
In the analysis of economic time series, a question often raised is whether a vector of variables causes another one in the sense of Granger. Most of the literature on this topic is concerned with bivariate relationships or uses finite-order autoregressive specifications. The purpose of this article is to develop a causality analysis in the sense of Granger for general vector autoregressive moving average (ARMA) models. We give a definition of Granger noncausality between vectors, which is a natural and simple extension of the notion of Granger noncausality between two variables. In our context, this definition is shown to be equivalent to a more complex definition proposed by Tjostheim. For the class of linear invertible processes, we derive a necessary and sufficient condition for noncausality between two vectors of variables when the latter do not necessarily include all the variables considered in the analysis. This result is then specialized to the class of stationary invertible ARMA processes. Further, relatively simple necessary and sufficient conditions are obtained for two important cases: (1) the case where the two vectors reduce to two variables inside a larger vector including other variables; and (2) the case where the two vectors embody all the variables considered. Test procedures for these necessary and sufficient conditions are discussed. Among other things, it is noted that the necessary and sufficient conditions for noncausality may involve singularities at which standard asymptotic regularity conditions do not hold. To deal with such situations, we propose a sequential approach that leads to bounds tests. Finally, the tests suggested are applied to Canadian money and income data. The tests are based on bivariate and trivariate models of changes in nominal income and two money stocks (M1 and M2). In contrast with the evidence based on bivariate models, we find from the trivariate model that money causes income unidirectionally.