Then 
(1 + b,B) 
Da Game Raa ea eet 
(1 + a,B + a7B~) 
aM (1 + b;B) é 
~ (1=yB)(1— 2B) 
o (1+) 1 _ lite) 1 : 
(GR) 0g) Taal” 
| 
Ms 
eS 
ES 
I ]+ 
Ils 
N — 
SS 
= 
mou, 
+ 
CaS 
ss 
ty 
+ 
iS |S 
——— 
R wn ‘ 
Mm 
el 
M2 — 
Green’s function is 
(5.124) 
(5.125) 
When 5; = 0, then Green’s function will be that of the AR(2) already given as Eq. 5.70. 
Green’s function can also be easily derived as a solution of the homogeneous equation, 
Eq. 5.120, 
(1 + a,B + a>B*)X, = 0 
with the initial conditions as follows. 
Substituting 
=0 
is 2) ioe) 
X;= ») Gj €1j = b> G; ake 
j=0 
into Eq. 5.123 gives 
(1 + a,B + apB?) p> Gj | E, = (14+ D,B)e, 
ar 
(1 + a;B + a2B*)(Go + GB + GpB? + G3B3 + - - Je, = (14+ d,B)€,. 
Comparing the coefficients of B on both sides of Eq. 5.127 shows 
136 
(5.126) 
(5.127) 
