When should I use the Breusch-Godfrey test instead of Durbin-Watson?

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AcadiFi · Accepted Answer

The Breusch-Godfrey test, also called the Lagrange multiplier test for serial correlation, addresses two major Durbin-Watson shortcomings.

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The procedure has three steps. First, estimate the original regression and save residuals e_t. Second, regress e_t on all original predictors plus p lagged residuals (e_{t-1}, ..., e_{t-p}), where p is the order you want to test. Third, compute the test statistic nR^2 from this auxiliary regression, which follows a chi-squared distribution with p degrees of freedom under the null of no serial correlation up to order p.

Suppose Desmond Okafor models Halverin Corp quarterly returns with a lagged return term plus macro variables. He suspects quarterly seasonality, so he runs Breusch-Godfrey with p=4. The test yields nR^2 = 14.8, compared against chi-squared(4) critical value of 9.49 at 5%. He rejects the null and concludes residual autocorrelation up to lag 4 exists.

The consequence is similar to what Durbin-Watson flags: standard errors are biased, t-stats unreliable, and inference invalid. Remedies include Newey-West HAC standard errors that adjust for both heteroskedasticity and autocorrelation, or explicitly modeling the autocorrelation with ARMA errors.

Breusch-Godfrey is now the default serial correlation diagnostic in most econometrics software because of its flexibility and validity in dynamic models.

When should I use the Breusch-Godfrey test instead of Durbin-Watson?

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