1 Durbin Watson Test
The Durbin-Watson statistic is a simple numerical method for
checking serialdependence. Let rk be the residuals sorted into time
order. Then the Durbin-Watson statistic is:
DW =n1
k=1(rk rk+1)2nk=1 r
2k
.
We have the following criterion:
DW < 2 2 > 2Decision Positive Serial Correlation NO serial
correlation Negative Serial Correlation
As a rough rule, serial correlations corresponding to DW outside
the range1.5 2.5 are large enough to have a noticeable effect on
our inference techniques.Note that DW itself is random and may be
outside the range 1.5 to 2.5, even ifthe errors are uncorrelated.
For data sets with long runs of units from the sametreatment, the
variance of DW is a bit less than 4/N.
In R, the durbin-watson test is located in library(lmtest):
> dwtest(formula) # z time index.
Figure 1: Durbin Watson Test
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