Breusch-Godfrey LM Test for Serial Correlation
Also known as: BG test, LM test for autocorrelation, Breusch-Godfrey serial correlation test, Breusch-Godfrey otokorelasyon testi
The Breusch-Godfrey test is a Lagrange-multiplier test for serial correlation in regression residuals, developed independently by Trevor Breusch (1978) and Leslie Godfrey (1978). Unlike the Durbin-Watson test, it detects autocorrelation up to any chosen order p, remains valid when the model includes lagged dependent variables, and produces a definite chi-square p-value rather than an inconclusive region — making it the modern standard for autocorrelation testing.
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When to use it
Use the Breusch-Godfrey test as the default check for serial correlation in time-series regressions, especially when the model contains lagged dependent variables or when autocorrelation beyond the first order is plausible — situations where the Durbin-Watson test is invalid or insufficient. Choose the order p to reflect the data frequency (for example, p = 4 for quarterly or p = 12 for monthly data to capture seasonality). It assumes the model is otherwise correctly specified; a rejection can in principle reflect dynamic misspecification rather than pure autocorrelation. When serial correlation is confirmed, report HAC standard errors or respecify the dynamics.
Strengths & limitations
- Tests autocorrelation up to any order p, capturing higher-order and seasonal patterns.
- Remains valid when regressors include lagged dependent variables, unlike Durbin-Watson.
- Yields a definite chi-square p-value with no inconclusive region.
- Computed easily as an auxiliary regression and widely implemented.
- Requires the user to choose the lag order p, which affects power.
- A rejection may reflect general dynamic misspecification rather than autocorrelation alone.
- Relies on an asymptotic chi-square approximation, so it needs a reasonable sample size.
- Diagnoses the problem but does not by itself provide the corrected estimates.
Frequently asked
Why use Breusch-Godfrey instead of Durbin-Watson?
Breusch-Godfrey tests autocorrelation up to any order, stays valid when the model includes a lagged dependent variable, and gives a clear chi-square p-value with no inconclusive region. Durbin-Watson only checks first-order correlation, is invalid with lagged dependent variables, and can be inconclusive.
How do I choose the lag order p?
Match it to the data: p = 1 for a basic first-order check, or p equal to the seasonal period (4 for quarterly, 12 for monthly) to capture seasonal autocorrelation. Reporting results for a couple of sensible orders is good practice.
What should I do if the test rejects?
Serial correlation leaves OLS coefficients unbiased but their standard errors wrong. Report HAC (Newey-West) standard errors, or respecify the dynamics (e.g., add lags) so the residuals become serially uncorrelated.
Sources
- Godfrey, L. G. (1978). Testing against general autoregressive and moving average error models when the regressors include lagged dependent variables. Econometrica, 46(6), 1293–1301. DOI: 10.2307/1913829 ↗
- Breusch, T. S. (1978). Testing for autocorrelation in dynamic linear models. Australian Economic Papers, 17(31), 334–355. DOI: 10.1111/j.1467-8454.1978.tb00635.x ↗
How to cite this page
ScholarGate. (2026, June 2). Breusch-Godfrey LM Test for Serial Correlation. ScholarGate. https://scholargate.app/en/econometrics/breusch-godfrey-test
Which method?
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