Geography Reference
In-Depth Information
The temporal autocorrelation can be defined as the correlation of the same
variable
X
between values at different time
s
and
t
.
E
[(
X
)(
X
)]
R
(
s
,
t
)
t
s
2
(2)
while
E
is the expected value operator,
is the mean of the observation
values and is the variance. The temporal autocorrelation can be used to
explore the time-series autocorrelation patterns.
With regard to the spatial dependence, spatial autocorrelation (association)
statistics have been used to analyze the degree of dependency among
observations in a geographic space (Cliff and Ord, 1973). These measurements
can be divided into two categories: global indices and local indices. Classic
global indices of spatial autocorrelation include Moran's I (1950), Geary's C
(1954), and Getis-Ord's General G (1992), while local indices of spatial
association (LISA) can be established by transforming the global indices into
corresponding local measurements based on different measures of similarity
(Anselin, 1995). All of these spatial autocorrelation statistics require a spatial
weights matrix that reflects the intensity of the geographic relationship
between observations and their neighbors, e.g., the distance-to-neighbor matrix
or the binary matrix in which the element value is 0 or 1 determined by
whether there is a shared boundary between the observation location and
neighbors. As suggested by Hardisty and Klippel (2010), adding the temporal
neighbors into the weights matrix would be one approach to extend the
traditional spatial autocorrelation measurements.
Here, we present three extended global measures of spatio-temporal
association regarding the spatial version of Moran's I, Geary's C, and Getis-
Ord's General G:
N
N
_
_
w
[
z
(
t
)
z
][
z
(
t
)
z
]
ij
i
t
j
t
i
1
j
1
I
st
N
N
w
t
t
ij
(3)
i
1
j
1
N
N
w
[
z
(
t
)
z
(
t
)]
2
ij
i
j
i
1
j
1
C
st
N
N
2
w
t
t
ij
(4)
i
1
j
1
