X,= 4,X,_1+ a Xiot...+ 4X44 & 
k 
= y a, X4+ &, (6.19) 
u=1 
Xx Cc Ci €1 
ners x, m 1,t eS 11,m .2,m ee wt 
X24 C2.14m C22.m €24 
More generally, in the P—dimensional process the dimensions X),, X21, .. . Xps 
are connected by feedback systems to each other. This process can be reduced to the P— 
dimensional AR(k) model, with k as an appropriate order, 
X,= 4, X1+ 4, X9+...4+ 4 X 4+, (6.20) 
X] Chim 2 0-0 Cip.m €1 
X2 Com, O06 C2p,m €2 
where X, =| | an=|°  \ €= 
Xp Colm : Cpp,m Ep, 
Eg. 6.20 can then be written 
k 
X; = yy Gy, Xim+ Ey, (6.20) 
m=1 
or 
k 
1- > an(B™)} X= &, (6.20”) 
m=1 
or a(B) X,= €,, 
here 
ag)=|1-{4 Z+anZ+ + a,2']| 6.21 
= 1 2 0%O°0 k . ( G ) 
207 
