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Data Analysis and Statistics for Geography, Environmental Science, and Engineering
book

Data Analysis and Statistics for Geography, Environmental Science, and Engineering

by Miguel F. Acevedo
December 2012
Beginner content levelBeginner
557 pages
19h 5m
English
CRC Press
Content preview from Data Analysis and Statistics for Geography, Environmental Science, and Engineering
384 Data Analysis and Statistics for Geography, Environmental Science, and Engineering
Matrix Φ is symmetric and has an inverse. Therefore, we can solve for coefcients a = Φ
−1
ρ.
For illustration, when AR(1) there is only one equation with obvious solution
ρ
()1
1
=
a (11.35)
For example, consider the series in Figure 11.16, the autocorrelation at lag 1 is ρ(1) = −0.48 and
relatively smaller for higher lags. Thus, we could model the series as AR(1), then solving Equation
11.35 we have a
1
= ρ(1) = −0.48.
When AR(2) we have two equations
ρρ
ρρ
()
()
() ()
11
21
12
12
=+
=+
aa
aa
(11.36)
in matrix form
ρ
ρ
ρ
ρ
()
()
()
()
1
2
11
11
1
2
=
a
a
(11.37)
Lag 1
zg.rts
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Publisher Resources

ISBN: 9781439885017