Diagnosing Serial Correlation in Forecasting Regression Residuals

Summary

The document describes a CPI forecasting regression whose author sees a moving average of the residuals moving in the same direction as CPI. The author asks whether this suggests omitted-variable bias, biased coefficients, or another modeling problem. The response attributes the pattern to an alleged adjustment in published government statistics and suggests that the errors may show positive serial correlation. This explanation is asserted rather than supported with evidence in the document.

For diagnosis, the response names the Durbin–Watson statistic as a test for first-order serial correlation and the Breusch–Godfrey test for higher-order serial correlation. The exchange does not report test results, establish that the residuals are autocorrelated, or explain whether the observed residual-target association implies coefficient bias. It is a short discussion with an unsupported proposed cause, so the tests are more directly reusable than the causal claim.

Key ideas

• The author observes that a moving average of regression residuals appears to move with CPI and asks what this implies.
• The response proposes an adjustment to published statistics as a cause, but provides no supporting evidence.
• Durbin–Watson is suggested for first-order residual serial correlation.
• Breusch–Godfrey is suggested for testing higher-order residual serial correlation.
• The document does not show test results or establish whether coefficients are biased.

Tags

# Assessing Forecasting with Correlated Residuals


# Assessing Forecasting with Correlated Residuals












Trying to use a linear regression model to forecast the CPI. I noticed that when I took a moving average of the residuals, though homoscedatisc and nonautocorrelated (i.e. they squiggle up&down with no uniform pattern), that they seemed to move in the same direction as the CPI. That is the moving average of the residuals and the depended variables correlated. What does this imply? Is this a case of omitted variable bias? Are my coefficients biased? What are some common prognoses for a such a problem?

## Answer by jeff m (score 1)

https://quant.stackexchange.com/a/7637

The reason you're seeing the bias is because of the adjustment, commonly referred to the "fudge factor" that they government applies to basically all of their published statistics. This is almost always in the direction to make the numbers rosier, and therefore your error term likely will exhibit signs of positive serial correlation.

The standard test for first-order serially correlated errors is the Durbin-Watson test statistic. For higher-order testing of serial correlation you can use the Breush-Godfrey test.

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.