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364 Chapter 10 Further Topics
Figure 10-11
Annual minimum water
levels of the Nile river
for the years 622-871.
Figure 10-12
The sample correlation
function of the data
in Figure 10.11.
Level
900 1000 1100 1200 1300 1400 1500
0 50 100 150 200 250
with {Zt} ∼WN(0, 5827.4) and modified AIC 2884.94. (The modified AIC statistic
for estimating the parameters of a fractionally integrated ARMA(p, q) process is
defined in terms of the Whittle likelihood LW as −2ln LW + 2(p + q + 2) if d is
estimated, and −2lnLW +2(p +q +1) otherwise. The Whittle likelihood was defined
in (10.5.10).)
In order to compare the models (10.5.11) and (10.5.12), the modified AIC value
for (10.5.11) is found as follows. After fitting the model as described above, select
ACF
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
0 10 20
Lag
30 40