Lecture Notes 7 Feb 2007 – STA 6934
Autocorrelation
In animal movement studies there has been some confusion in the
literature over what is meant by autocorrelated observations of locations.
1) Observations are independent in the statistical sense when the time
points at which locations are recorded are sampled at random from the
time interval of the study. The locations observed are then random
selections from some unknown bivariate distribution.
The steps we observe from the random selection may or may not appear
to be correlated when the data were sampled at random – the reasons?
The observations will appear uncorrelated if the time period from which
the sample is taken is very large relative to the random sample size. On
the other hand, if the sample is small relative to the time period under
study, then directed movements, behavior, the fact that movement is a
correlated random walk, etc. can all conspire to make the data appear
correlated. See the examples on page ___.
2) There is independence in the sense that a measure of correlation is
statistically insignificant.
Notation: Suppose an animal is tracked so that its position (
X
i
,
Y
i
),
i =
1
,
…,N
is recorded every
∆
t
time units. Then our data consist of the walk
{(
X
0
,
Y
0
), (
X
1
,
Y
1
), (
X
2
,
Y
2
), …, (
X
N
,
Y
N
)}.
Independent Observations when no correlation in the walk
In a walk in which the new position at time
i
does not depend in any
way on the location at time
i –
1 the locations are independent of one
another.
We could denote this as
y
i
y
i
x
i
x
i
Y
X
ε
μ
ε
μ
+
=
+
=

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