Therefore Igl=V, (5.147) 
Arg[g] = jw +o. (5.148) 
From Eq. 5.143 G; can be expressed as a damping cosine curve with damping y = Vay 
determined by a> and the period by 
20 _ 27 
SS == =F 
® cos! 
2Vap 
After a2 was fixed, period is decided by a, and phase that is 6 different from that of 
a,—2b, 
| 4a2-a? 
11,2 by 6 = tan™! , as is shown in Fig. 5.24. 
Fig. 5.24. G for ARMA(2.1). 
Green’s function and the autocovariance function are closely related as expected, because 
using Green’s function, 
R(r) = E[xX, X,-r] 
= oc > G; Gjsr- (5.149) 
5.2.4.2 Inverse Function of ARMA(2.1). In Eq. 5.123 
(1 +a, B + a2 B*)X, = (1+, B)€;. 
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