基于DAG方法的SVAR模型识别: 理论基础和仿真实验

在递归结构假设条件下，文章证明了SVAR模型与线性动态因果结构模型是相同的数据生成过程，且SVAR模型中的同期变量系数矩阵结构与同期变量为节点的DAG之间存在特定的对应关系；文章还证明：给定真实的数据生成过程为线性动态因果结构模型，从数据出发，利用现有的IC，SGS，PC等因果结构推断算法可以对同期变量为节点的DAG作出正确推断，且这一结论不依赖于变量服从联合高斯分布，从而在理论上证明了基于DAG方法构建SVAR模型识别条件的可行性，并给出该方法下SVAR模型识别的充要条件；最后，Monte Carlo仿真结果显示：在扰动项服从不同分布条件下，基于DAG方法在构建正确的SVAR模型识别条件方面均有着非常好的表现，SVAR模型识别的充要条件也得到了仿真结果的有力支持.

Identification of SVAR model based on directed acyclic graphs: Theory and Monte Carlo simulation

This paper proved that, based on the data generated by the linear dynamic causal model, the present alogrithms of causal infernce just as IC, SGS or PC alogrithm can be used to explore the true causal structure between contemporaneous variables correctly, and this result is not dependent on the assumption that the disturbance terms in the dynamic causal structure model are normally distributed. Furthermore, the paper demonstrates that the SVAR model and the linear dynamic causal model are the same data generating process under the assumption of recursive structure, and there are corresponding relations between the coefficient matrix of contemporaneous variables in the SVAR model and the causal structure of contemporaneous variables in the linear dynamic causal model which is a DAG. Therefore, We have established a theoretical basis for the method of identifying the SVAR model based on DAG. The paper has also given a necessary and sufficient condition for identifying SVAR model with the method. Futherly, the results of Monte Carlo simulation have supported all of those conclusions.