Fig. 5.22c. Estimated by nonparametric method. 
Fig. 5.22. (Continued) 
5.2.4 Second Order Autoregressive First Order Moving Average 
Process, ARMA(2.1) 
More generally for AR(2), when the residual series €; of X;, obtained by subtracting 
the part which is linearly dependent on X;_1, 
6 =X,—-a, X:-1 (5.117) 
was correlated not only with X,_2 as for AR(2) but also with €,_; as shown in Fig. 5.23. 
€t € 
t 
(a) Et VS. Xt-2. (b) et vS. € 44 
Fig. 5.23. Characters of €: for ARMA(2.1). 
Then 
6 = a4 X24+ dE +& « (5.118) 
134 
