Then the spectrum is 
Se (@ 
sx(@) = — (6.22) 
lace) 
2m - ay e”_ a> GMs. 6 =O GD 
where 
ERE Ne aa (6.23) 
€; €,] = ¢ 
yy t=0. 
The order k can be obtained from Akaike’s minimum AIC criterion in this case too; 
i.e., we can find k that minimizes 
AIC (p,k) = Nlog bu. | + 2p*k, (6.24) 
where 
k 
>) = > @mRx(m), (6.25) 
m=0 
as it was for the scalar case. 
Through these procedures, after fixing the order k, we get the coefficient 
a, ... Q,,as for the scalar case. Then we can get the spectrum matrix from Eq. 6.22. 
Srasa Sx 2 8 Sxix, 
Sxx; Sx 6 06 Sixx, 
: ; (6.26) 
The cross spectrum, for example S,,x,(w), is obtained in complex form 
Sx,x,(@ )= Cox,x,(@) a7 iOx 1%2(@) (6.27) 
as an element of the spectrum matrix, Eq. 6.26. 
208 
