st 
j —_ 
Fig. 5.44. Residual error. 
Sometimes, however, it is not easy to determine the order because the rate of change 
does not show clearly by this method. 
5.5.2 Partial Autocorrelation Method 
If a,, denotes the ith autoregressive parameter of an AR() process, then the auto— 
correlation coefficient 9; is from Eq. 5.220, 
Qi = — 4n1Qi-1 — 2720i-2° * 
p12 in 
which gives the Yule-Walker equations, 
Q1 =—4n100—4n201°- 
02 =—4n101—-4n200° - 
On = — GniOn-1 — 4n,Or2°- 
*— Ann Qi-n 
(5.247) 
*— Ann Qr-1 
*— Ann On-2 (6 248) 
*—GAnnQo- 
Then, the last coefficient a,,, of the fitted AR(7) model is called the partial autocorrelation 
Qn, forn = 
Since 0, = 1, from Eq. 5.248, 
—411=01>01' 
1, 2- - - , and will be used*” to suggest the order of the AR model. 
11 
Q1 Q2 ao 
Sipe EE = (5.249) 
1 01 (Gil 
Oxeel 
194 
