This is the same as adopting the least squares estimate as already mentioned. That is 
obtained from 
) 
O2 La 
Ou 
and 
F) 
ag Fete cen 
0a; 
as 
N 
S. [&-m) + arKer—w) +: + + ayKen—H)} = 0 (5.235) 
t=n+l 
and 
N 
y {(X-w) +a(X-1-M) + - + af(X,j;—M)- > > +a,(Xpn—/) |X j-w = 0. 
ci ec (5.236) 
From Eq. 5.235 
fi oeeeenhenioe sera (5.237) 
1+a,+d.+:--+4, 
where 
oy all Ny 
t=nt+l 
N 
= a el 
When n is small compared to Nj, X; will be close to X = N » X, and Eq. 5.237 will be 
t-1 
pi=X. (5.238) 
From Eq. 5.236 
Ny a a — —_— 
{Op -¥) + bi Kea-H) ++ + GK j-K)- +4, (Kin-B] x 
t=n+l 
{Xj-H}=0, fal --n. 
Here, if we approximate further, under the assumption that & is also small in relation to N, 
then 
N 
DY Xia X\Xj-X) = NRG-8), 
t=n+l 
and Eq. 5.236 becomes 
191 
