结构VAR的有向非循环图模型

Directed Acyclic Graph Modeling for the Structural Vector Autoregression

研究用图模型方法辨识结构向量自回归(VAR)模型,图中的结点表示不同时刻的随机变量,结点间的边表示其所表示的随机变量之间存在的因果相依关系.针对建立有向非循环图的问题,提出了一种基于回归分析的判断方法,用回归方程的回归平方和之差作为统计量,确定当前变量之间相依关系的方向.与R ea le的逐一判别法和A lessio的图搜索方法相比,文中提出的基于统计分析的方法简单易行,且可获得唯一的当前变量有向非循环图.最后以两组模拟序列为例,验证了所提出的方法是可行且有效的.

In the problem of identification Structural Vector Autoregression using graphical models, the vertices denote random variables in different times, and the edges denote there exist causal dependence relations between the variables denoted by the vertices. A method to determine the direction of the relationships of the current variables is presented. The method is based on the theory of variable selection in regression analysis. The test statistics is the difference between the sums of regression square in the regression equation. Compared with the methods presented by Resle and Alessio, the method based on statistics can be performed easily and lead to unique directed aeyelie graph for the current variables. Finally, two simulation examples show the practicability and efficiency of the method presented in this paper.