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March 22, 2005
Serially Correlated Error Terms
We worked our way through some algebra that does not appear in the textbook. The first step was showing how the coefficient estimate is a function of the random error terms.
If the errors and regressors are not independent, you get bias in the estimate of beta.
The standard formula for the variance of a regression coefficient assumes that the errors are independent. If they are not, this formula leaves out some nonzero terms.
On the left, diagnosing serially correlated errors. In the middle, what happens if you have serially correlated errors. On the right, time series economic data is all serially correlated so it is easy to see why the errors from time series regressions might be as well.
The distribution of the Durbin-Watson statistic under the null of no serial correlation:
Side trip: One important application of the covariance is in determining the risk of a portfolio containing two assets.
Posted by bparke at March 22, 2005 08:50 PM