Why Autocorrelated Errors Undermine Regression Inference
Summary
The document explains why autocorrelation matters in time-series regression. It distinguishes two consequences of violations of the usual least-squares assumptions: heteroskedasticity can make standard errors and resulting inference unreliable, while autocorrelation in errors can also distort coefficient estimates. The discussion frames autocorrelated residuals as evidence that a model may leave useful structure unexplained, and suggests adding autoregressive terms to capture it.
For financial analysis, it notes that modeling returns instead of price levels is a basic practice, while emphasizing that returns should still be checked for autocorrelation. The document does not provide a specific diagnostic procedure, worked example, or comparison of correction methods; it points to further discussion of handling low-order autoregressive errors. Its advice is therefore a conceptual introduction rather than a full modeling workflow, and whether a correction is appropriate depends on the model and data.
Key ideas
- Autocorrelation in regression errors can affect coefficient estimates, not only standard errors.
- Heteroskedasticity can invalidate conventional standard errors and make inference unreliable.
- Persistent residual autocorrelation may indicate that relevant time-series structure is missing from a model.
- Adding autoregressive terms is one way to explain correlated errors.
- Financial analysis often uses returns instead of prices, but returns still require autocorrelation checks.
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Full text
# Who cares about autocorrelation?
# Who cares about autocorrelation?
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 by Dirk Eddelbuettel (score 10, accepted)
https://quant.stackexchange.com/a/1313
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 by Zarbouzou (score 4)
https://quant.stackexchange.com/a/1312
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.