Durbin-Watson Test for Autocorrelation
Also known as: DW test, Durbin-Watson statistic, Durbin-Watson otokorelasyon testi
The Durbin-Watson test, developed by James Durbin and Geoffrey Watson in 1950–1951, detects first-order serial correlation in the residuals of a linear regression. Its statistic ranges from 0 to 4, with a value near 2 indicating no autocorrelation, values toward 0 indicating positive autocorrelation, and values toward 4 indicating negative autocorrelation. It remains one of the most reported regression diagnostics despite well-known limitations.
Key highlights
- Simple, fast, and reported automatically by essentially every regression routine.
- Directly interpretable scale: near 2 is clean, below 2 is positive autocorrelation, above 2 is negative.
- Effective as an immediate first-pass diagnostic for time-ordered residuals.
- Historically well understood, with tabulated bounds available for many sample sizes.
Intuition
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How it works
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When to use it
Use the Durbin-Watson test as a quick check for first-order autocorrelation in the residuals of a time-ordered OLS regression, especially as a first diagnostic when reading regression output. It is appropriate only when the regressors are strictly exogenous and the model does not include a lagged dependent variable — in that common case the statistic is biased toward 2 and Durbin's h or, more generally, the Breusch-Godfrey LM test should be used instead. Because it targets only first-order, AR(1)-type correlation and can land in an inconclusive region, the Breusch-Godfrey test is preferred whenever higher-order autocorrelation is plausible or a definitive p-value is required.
Strengths & limitations
- Simple, fast, and reported automatically by essentially every regression routine.
- Directly interpretable scale: near 2 is clean, below 2 is positive autocorrelation, above 2 is negative.
- Effective as an immediate first-pass diagnostic for time-ordered residuals.
- Historically well understood, with tabulated bounds available for many sample sizes.
- Detects only first-order autocorrelation, missing higher-order or seasonal patterns.
- Has an inconclusive region between the tabulated bounds where no decision can be made.
- Invalid when the model contains a lagged dependent variable, being biased toward 2.
- Assumes strictly exogenous regressors and normally distributed errors for the exact bounds.
Common pitfalls
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Applications
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Frequently asked
What value of the Durbin-Watson statistic is 'good'?
A value close to 2 indicates no first-order autocorrelation. Values meaningfully below 2 indicate positive autocorrelation (the common concern), and values above 2 indicate negative autocorrelation. As a rough guide, values roughly between about 1.5 and 2.5 are often considered unproblematic, but formal bounds should be consulted.
Why is my Durbin-Watson result 'inconclusive'?
Because the exact distribution depends on the regressors, the test uses lower and upper critical bounds. When the statistic falls between them, neither rejection nor non-rejection is justified. In that case use the Breusch-Godfrey LM test, which yields a definite p-value.
Can I use it with a lagged dependent variable?
No. When the model includes a lagged dependent variable the Durbin-Watson statistic is biased toward 2 and will tend to miss autocorrelation. Use Durbin's h statistic or, preferably, the Breusch-Godfrey test instead.
Sources
- 1.Durbin, J., & Watson, G. S. (1950). Testing for serial correlation in least squares regression: I. Biometrika, 37(3/4), 409–428.
- 2.Durbin, J., & Watson, G. S. (1951). Testing for serial correlation in least squares regression: II. Biometrika, 38(1/2), 159–178.
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Cite this page
ScholarGate. (2026, June 2). Durbin-Watson Test. ScholarGate. https://scholargate.app/econometrics/durbin-watson-test