数据分析 时间序列分析 ARMA模型

一.概念
1.概念:

具有如下结构的模型称为自回归移动平均模型(Auto Regression Moving Average Model;ARMA Model),记为$ARMA(p,q)$:$$\begin{gathered} x_t={\phi }_0+{\phi }_1{x}_{t-1}+{\phi }_2{x}_{t-2}+...+{\phi }_p{x}_{t-p}+{\epsilon }_t-{\theta }_1{\epsilon }_{t-1}-{\theta }_2{\epsilon }_{t-2}-...-{\theta }_q{\epsilon }_{t-q} \\ s.t.\{\begin{array}{l}{\phi }_p,{\theta }_q\ne 0\\ E({\epsilon }_t)=0,D({\epsilon }_t)={\sigma }_{\epsilon }^2,\gamma ({\epsilon }_t,{\epsilon }_s)=E({\epsilon }_t{\epsilon }_s)=0(s\ne t)\\ Cov(x_s,{\epsilon }_t)=0(s<t)\end{array} \end{gathered}$$