Suppose that the two variables are integrated of order one, $1(1),$ and cointegrated. Using the cointegrating relation of z$,=$ y $-$ Ax $($ a $>0),$ we can modify the above VAR model into the following vector error correction model $($VECM$).$

Ax$,=$ Y$1$x$-1+$Yzdx$,-2$t Yy$1$ay$,-1$ t Yy$2$ay$-$z $+812-$t&e Ay$,=$ y$1$Ax$1-1$t$8$x$2$Ax$-2$ty$1$y$-1+$yzy$-2+02$z$-1$tEze