There is much in the literature about time-series and the problem of auto-correlation. Unfortunately the issue of why auto-correlation is actually troublesome is glossed over, and methods for testing a time-series for auto-correlation are presented. Basically, it is assumed that auto-correlation is bad for purposes of analysis.

What assumptions does the presence of auto-correlation violate for downstream analysis (eg, i.i.d) and what are some practices for dealing with the issue?

• Of course publications gloss over this, as it's considered general knowledge among the readership of the paper. – Jase Dec 7 '12 at 16:25

Just about every introductory Econometrics class teaches that the violations of BLUE ("Best Linear Unbiased Estimator" -- the properties of linear least squares) are

• invalid standard errors in the case in the heteroscedasticity, so while your parameter estimates are still valid ("unbiased") your inference may be off

• invalid estimates (!!) in the presence of autocorrolated errors, so your actual parameter estimates may be off, and that can be a big deal.

Libraries have been filled with this material so I won't start rehashing it. A real nice discussion of how to account for AR(1) and AR(2) errors when estimating a linear trend was recently provided here (via R Bloggers).

One of the most basic fixes in Finance is to work on returns rather prices, but you still want to check.

Autocorrelation is usually a problem when you are doing the analysis of your error terms. When you build a model, you expect that the error term will have non significant autocorrelation. It is simple to understand: If your error term still have autocorrelations it certainly means that you are missing some information that could be introduced in your model. A standard approach to get rid of it is to incoporate autoregressive factors that could explain the autocorrelations in the errors terms.

• Are error terms and residuals similar? As far the terms having significant autocorrelation, does that tell you that your model is naive or maybe you don't understand the problem sufficiently to create a model in the first place? – Milktrader Jun 17 '11 at 16:36
• @Milktrader: error terms and residuals are synonyms. If the residuals are autocorrelated, you should first reconsider your model specification. Any good book on applied econometrics (specifically time-series) should have a chapter on model specification. I've found Kennedy to be a useful reference. – Joshua Ulrich Jun 18 '11 at 11:51