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Testing for Serial Correlation (Without Strong Exogeneity (Null Hypothesis…
Testing for Serial Correlation
Without Strong Exogeneity
Null Hypothesis - No Serial Correlation
Form an estimated residual by running the standard regression
Regress the estimated residuals on each other
including all of the explanatory variables that are in the same time period as the dependent variable
By including the
explanatory variables
we are controlling for any potential correlation between error term and residual
Test the significance of the coefficient using a
t-test
If we
reject the null
then we conclude that errors
are serially correlated
If we
fail to reject the null hypothesis
then we conclude that errors
are not serially correlated
If we suspect there is
heteroskedasticity in the auxiliary regression
then we must use robust standard errors when carrying out the test
This ensures that the t-stat will be t-distributed
When we don't have strong exogeneity and a lagged time variable we will have an inconsistent and biased estimation of b therefore an inconsistent and biased estimation of Û.
With Strong Exogeneity
Null Hypothesis - No Serial Correlation
We are unable to directly observe the residual therefore we need to form an
estimated residual
by running the standard regression
Once we have estimated of consecutive residuals we then
regress Ut on U(t-1) to form an estimate of the coefficient
Carry out a
t-test
to test the significance.
If we
reject the null
then we conclude that errors
are serially correlated
If we
fail to reject the null hypothesis
then we conclude that errors
are not serially correlated
If we suspect there is
heteroskedasticity
then we must use robust standard errors when carrying out the test
Yt = X'b+ Ut => Û=Yt-X'b
As under the null we have
homoskedasticity
OLS is efficient and the
Gauss-Markov Properties are satisfied
. We are also
able to use the t-distribution
Testing for Higher Order Serial Correlation
Null Hypothesis - No Serial Correlation
Form the residual from the standard regression
Carry out the auxiliary regression to form estimates of the coefficients
test the joint significance of the coefficients using an
F-Test
If the coefficients are
jointly insignificant
then we can
reject higher order serial correlation
If the coefficients are
jointly significant
then we have evidence of
higher order serial correlation
and
reject the null hypothesis