Figure 5.21a shows the theoretical autocorrelation coefficient @(r) = R(r)/R(O) of 
this generated AR(2) process, calculated by Eq. 5.90, using the values of coefficients 
a; =-0.5, a7 = 0.8, and the variance a? = 1.0. Part b of the same figure shows the 
estimated 0(r) = R(r)/R(O), actually calculated from the generated process. An AR(n) 
model was fitted and its order was searched by AIC criteria and found to be n = 2. Then 
parameters were estimated by the method described in this section by Eqs. 5.103’ and 
5.108. The results were 
a; =—0.54156, d> = 0.81838, anda2= 1.04702, 
which are close to the values actually used in generating the process. The autocorrelation 
coefficients were estimated from Eq. 5.90 using these values just as were the theoretical 
values. The results were quite similar and very close to the theoretical values in 
Fig. 5.21a, so again the drawings were omitted. 
-1.0 j T T T 1 
0.00 7.50 15.00 22.50 30.00 37.50 45.00 52.50 60.00 
7T 
Fig. 5.21a. Theoretical. 
Fig. 5.21. Autocorrelation coefficient for AR(2) process 
X,-0.5 X,_, + 0.8 Xo =€1, Er: N[O, 1]. 
131 
