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ECON346 (Econometrics)
Week1314 Page 1
Serial Correlation (autocorrelation)
Serial correlation is usually associated with time series data, but can occur in cross
sectional data also, in which case it is called spatial correlation (correlation in space
rather than in time).
The classical assumption:
i
j
E(
)=0
or
( )
0
if
ij
E r
i
j
ε ε
=
≠
If the current observation of the error term is function of the previous observation of the
error term (violation of classical assumption):
For a time series example (first order serial correlation):
1
t
t
t
u
ε
ρε

=
+
Property of
ρ
(the strength of the serial correlation)
1.
1
1
ρ
 <
<
2.
ρ
= 0 means no serial correlation.
3 .
As the absolute value of
ρ
approaches to 1 means a high degree of serial correlation
1. Reason for the serial correlation
Pure Serial Correlation: The most economic time series exhibit some cyclical behavior
and successive observations are likely to be interdependent or correlated. GNP,
employment, money supply price indexes
Impure Serial Correlation: caused by specification error like omitted variables or an
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 Spring '11
 Wang

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