Oh | Oe oom cy or 
Cie ein aamen Or=si02 
1 @n1 
Or-1 On-2 On-3°°° Q1 On 
ci we Abt ELA CANE NS SS: (5.249") 
ID Oi) Ore C2 Ot 
Q1 1 @1-°-*@n3 Qn2 
1) @A 
Or-1 Qn2On3°°°OQ1 1 
A plot of 0;'02'- - -@,' against n is called the partial autocorrelation function diagram. 
If the true order was n, 0,’ Or — a; ; Should vanish for k > n and the plot of the partial 
autocorrelation should show the real order 7. 
For this purpose, a recursive method for calculating 9,’ when — dp, are estimated 
from Yule—Walker equations has been given by Durbin? as 
Qn+1oj = Gn j—Ansine1 Gann jis J=l,---n (5.250) 
6(m+1)- > 4, ,6(n+1-j) 
: (5.251) 
Qm+1,n+1 = 
j= 
j=1 
553 Visual Inspection of the Autocorrelation 
As has been shown in the preceding sections, the types of models and their orders 
are well reflected in the pattern of the curve of the autocorrelation function. For example, 
for the MA(m) model, the correlation cut down to 0 after the lag m, and for the AR(7m) 
model, the correlation has the form of damping oscillations. Box and Jenkins*’ have 
developed this method and showed many examples of estimating the order from these 
patterns. However, it requires skill and long experience to be able to estimate the actual 
order correctly by this inspection. 
195 
