Econometrics lecture notes on Serial Correlation.
You must know what positive and negative serial correlation are (Page 29)
The implications for OLS estimates: They are in general unbiased when we have serially
correlated error terms, except when we have a lagged dependent variable in which case
they are biased. However the t statistics are biased upwards hence we are likely to accept
as significant variables which in fact are not. Finally there is a better more efficient
estimation technique. This is the method of generalised least squares (GLS) described in
the notes. The GLS estimator is
ΒGLS = (X'V-1X)-1X'V-1Y
(1)
For the general linear model: Y= XΒ + u
You should know (1), but not to derive it. You should also know what V looks like when
we have first order serial correlation of the form ut = ρut-1 + εt as defined half way down
page one of your notes. V is given in (3) on page 30. You should also know (4) and (5)
on page 31. But not the rest of page 31 or the first half of 32. You should know what the
Durbin Watson statistic is and how to test for positive and negative serial correlation.
You should also know that GLS when we have serial correlation is equivalent to the
process described at the top of page 35.
Heteroscedasticity
The formula
ΒGLS = (X'V-1X)-1X'V-1Y
(1)
Can also be used when we have heteroscedasticity. You should know what
heteroscdestacity is and again what V is in the formula (1). It is defined at the bottom of
page 35 (in fact it is σ2Ω). You should also understand page 36.