On slide 19 of Chapter 2, I asserted that the point estimates
produced by lm()
are “good” but the usual ordinary least
squares (OLS) standard errors and associated tests are “junk”. The
justification was that the estimator is unbiased regardless of the
correlation structure, but its variance depends on a particular
assumption about the correlation (i.e., independence) that is
inconsistent with the sample ACF. However, this is not quite enough to
dismiss the OLS standard error estimates. It could be that in this
particular situation the standard errors are not sensitive to the model
violation, in which case the OLS standard errors might be a useful
approximation. Alternatively, the OLS standard errors might be
substantially wrong. How could you investigate that, given your current
level of understanding of statistical methods? Imagine the issue arose
in a statistical consulting situation where you are supposed to give an
immediate suggestion of how to proceed.