Who cares about autocorrelation?

Question

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?

Answer 1

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.

Answer 2

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.