the 90% level of confidence interval of this estimate, based on the y*—distribution of the 
equivalent degree of freedom (here approximately equal to 27) as is explained in Section 
2.5.5 is shown as vertical lines for reference. 
5.2.3 Autoregressive Process of the Second Order, AR(2) 
As was shown in the last section for the AR(1) process, the residual part €, of X;, 
obtained by subtracting the linearly dependent part aX,_; from X 1, 
€,= X;—aX;1 Gia) 
was a purely random process uncorrelated with€ 1, €;2: - - aS in Fig. 5.13a and uncor- 
related with X;_2, X;3- - - aS in Fig. 5.13b. 
0 > e., 
Fig. 5.13a. ©, vs. €,_, for AR(1). 
X2 
Fig. 5.13b. ©, vs. X,-> for AR(1). 
Fig. 5.13. Characters of €, for AR(1). 
Go = 0 
El€,- €++) = Ele,-X;2] = 0. 
If this relation does not exist and the residual €;, that is, 
€;/ = X,-a'X,-4, (5.57) 
was linearly correlated with X,_2 as in Fig. 5.14, then 
117 
