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October 27, 2005
Serially Correlated Errors - I
A favorite explanation for serially correlated errors is that the errors are really just unobserved left-out variables and economics time series variables tend to be serially correlated.
To justify these calculations
we need these assumptions and conclusions
The derivation looks something like this:
If the errors are serially correlated the derivation above is invalid because the covariance terms do not equal zero.
The bottom line is that the standard calculations assume that the errors are serially independent and, therefore, that the covariance terms can be dropped. If the errors are serially correlated, the formula for the standard error is wrong. Given that serial correlation tends to be positive, the standard error formula leaves out positive terms, causing the calculated result to be too small and causing the t ratio to be too large.
Posted by bparke at October 27, 2005 08:35 PM