图模型方法及ARMA模型检验

Graphical modeling for test of ARMA model

应用图模型方法来研究时间序列中的因果关系,并以ARMA(1,1)时间序列为例作了说明.将ARMA模型表示成混合图,证明了ARMA模型的系数就是在移去了时间序列中其他成员的线性效应后的偏相关系数.这样就可运用通常的图模型推断算法来做参数估计和预测.与传统的对ARMA模型的检验法相比较,该方法既直观又易于计算.

Graphical modeling is a new statistical method in recent times. It is the one of hot points recently for applying graphical models to time series in mathematical statistics. In this paper, we analyze the causality in time series with graphical models, and discuss the classical ARMA （ 1,1 ） model as an example. The ARMA models are expressed as mixed graphical models, and then we show that the coefficients of ARMA model are the partial correlation coefficients after removing the linear effects of the other components of the time series. Thus a new approach is proposed to parameter estimation and test with the common graphical modeling inferential procedure. Compared to the traditional test method for ARMA models, our method is intuitive and very simple in computations.