The values of parameters by (and bz, a, if any) and of Ge estimated, and also of 
estimated d,---d, of AR(n) models are listed in Table 5.2. By comparing Fig. 5.37 and 
Fig. 5.40, we can find the difference of the pattern of the spectra by the difference of the 
sign of parameter b;. The same tendency appears in the difference between Fig. 5.27 and 
Fig. 5.30. We can recognize this difference also in comparing the original form of the 
generated processes in Fig. 5.35 and Fig. 5.38, and Fig. 5.25 and Fig. 5.28. 
Figures 5.41, 5.42, and 5.43 show the results for a generated ARMA(2.2) model. Its 
time history readings are listed in Appendix Al as Table A1.9; pp. 251 and 260. The fig- 
ures are the same as for the other examples, so no explanation will be given here. The 
estimated values of parameters dp, Bn. andG? are listed in Table 5.2. The optimum m, n 
for a fitted ARMA(n,m) model appeared to be n = 2, m= 2 by AIC cniteria for this case 
too. In this case G2 appeared to be 0.84312, quite different from a2 = 1.0, but we could 
not find the reason or the error for their poor estimation. 
5.00 
-5.00 T T T 7 7 T T 7 T : 
0.00 75.00 150.00 225.00 300.00 375.00 450.00 525.00 600.00 
ft 
5.00 - 
2.50 4 
0.00 
-2.50 4 
-5.00 
100 150 200 250 
= 
Fig. 5.41. Simulated ARMA(2.2) process 
X,— 0.5X,, + 0.8X,. = €,+ 0.2€,,+0.8€,2,  €,: N[O, 1]. 
176 
