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22 Chapter 1 Introduction
ACF
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
Figure 1-15
The sample autocorrelation
function for the Lake
Huron residuals of
Figure 1.10 showing
the bounds ±1.96/ √ n.
0 10 20
Lag
30 40
Figure 1-16
Scatter plot of
(yt−1,yt ), t 2,...,98,
for the data in Figure 1.10
showing the least squares
regression line y .791x.
outside the bounds ±1.96/ √ 97 at lag 1 ( ˆρ(1) .216), but it is inside the bounds for
all other lags up to 40. This check that the estimated noise sequence is consistent with
the iid assumption of (1.4.3) reinforces our belief in the fitted model. More goodness
of fit tests for iid noise sequences are described in Section 1.6. The estimated noise
sequence {zt} in this example passes them all, providing further support for the model
(1.4.3).
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-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5