How do I use the Durbin-Watson statistic to test for autocorrelation?

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AcadiFi · Accepted Answer

The Durbin-Watson statistic tests for first-order autocorrelation in regression residuals. Its formula approximates DW = 2(1 - rho).

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Formal testing requires comparing DW against lower (d_L) and upper (d_U) critical values from Durbin-Watson tables, which depend on n, k, and significance level. The decision regions are: if DW < d_L, reject null of no positive autocorrelation; if DW > d_U, fail to reject; between them is inconclusive. For negative autocorrelation, mirror the logic around 4.

A DW of 1.2 with n=60 and k=3 at 5% significance has d_L roughly 1.48 and d_U roughly 1.69. Since 1.2 < d_L, you reject the null and conclude positive autocorrelation exists. Consequences include underestimated standard errors, inflated t-stats, and misleading significance tests.

Imagine Ashok Verlain regresses monthly Grayholm Bank revenue on macro factors. Positive autocorrelation suggests omitted dynamics, perhaps a lagged revenue term or seasonal pattern. Remedies include Newey-West standard errors, autoregressive error models, adding lagged dependent variables, or first-differencing the data.

DW is limited: it only detects first-order autocorrelation and fails when lagged dependent variables appear. For broader diagnostics use the Breusch-Godfrey test.

How do I use the Durbin-Watson statistic to test for autocorrelation?

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