向量自回归模型Granger因果图的条件互信息辨识与应用

Identification and application about Granger causality graph of vector autoregressive model using conditional mutual information

Granger因果性是衡量系统变量间动态关系的重要依据.传统的两变量Granger因果分析法容易产生伪因果关系,且不能刻画变量间的即时因果性.本文利用图模型方法研究时间序列变量间的Granger因果关系,建立了时间序列Granger因果图,提出了Granger因果图的条件互信息辨识方法,利用混沌理论中的关联积分估计条件互信息.统计量的显著性山置换检验确定.仿真结果证实了方法的有效性,并利用该方法研究了空气污染指标以及中国股市间的Granger因果关系.

The Granger Causality is an important basis for measuring the dynamic relationships among system vari- ables. Traditional two-variable Granger causality analysis method is prone to inducing spurious causal relationship and can not portray the immediate causal relationship. This paper explores how to use graphical models method to analyze the Granger causal relations among components of multivariate time series. Granger causality graph of time series is presented. The structural identification of Granger causality graph is investigated based on the conditional mutual information. The conditional mutual information is estimated using the correlation integral from chaos theory. The significance of the tested statistics is determined with a permutation test. The validity of the proposed method is confirmed by simulations analysis. The Granger causal relationships of the air pollution index and the China＇s stock market are investigated using the proposed method.