DurbinWatson

The Durbin-Watson statistic, commonly abbreviated as DW, is a regression diagnostic used to detect the presence of first-order autocorrelation in the residuals of a linear regression model. It was developed by James Durbin and Geoffrey Watson in 1950. The statistic is defined as DW = sum_{t=2}^n (e_t - e_{t-1})^2 / sum_{t=1}^n e_t^2, where e_t are the estimated residuals from the regression.

DW values range from 0 to 4. A value near 2 indicates little or no first-order autocorrelation. Values substantially below 2 suggest positive autocorrelation, while values substantially above 2 suggest negative autocorrelation. Values near 0 or near 4 indicate strong positive or negative autocorrelation, respectively.

DW is specifically a test for first-order serial correlation in the regression residuals. Its exact distribution under the null hypothesis of no autocorrelation depends on the design matrix and sample size, so critical values are typically obtained from tables or approximations rather than simple p-values. Because the distribution is nonstandard, especially when lagged dependent variables are included as regressors, practitioners often use complementary tests such as the Breusch-Godfrey test to assess higher-order serial correlation.

Interpretation guidelines emphasize that DW does not test overall independence but focuses on first-order autocorrelation. A DW value far from 2 signals potential model misspecification, omitted variables, or measurement error, and may prompt model refinement. The Durbin-Watson statistic remains a common tool in econometrics and applied statistics for regression diagnostics.