QUESTION:

Can you tell me what the advantages and/or disadvantages are of using a regression on residuals

procedure to control for time in time series regression against the more usual method of including time

as an independent variable?

ANSWER:

What should be done is to incorporate contemporaneous and lagged effects of possible exogenous series

and then to add whatever noise structure is necessary. The noise structure could be as simple as an

adjustment for an unusual value, or a seasonally "usual value", or a level shift or a time trend(s).

Additionally, there may be some stochastic or probabilistic component that might be needed such as an

AR(1) process or more generally an ARIMA process.

Don't despair AUTOBOX speaks to these issues as it tests and automatically adjusts for these potential

violations of the Gaussian assumptions.