DurbinWatsontest

The Durbin-Watson test is a statistical procedure used to detect the presence of first-order autocorrelation in the residuals from a regression analysis. It is widely applied in econometrics and time-series analysis to assess whether the error terms are correlated across adjacent observations, which can affect standard errors and hypothesis tests.

The test statistic is defined as d = sum_{t=2}^n (e_t − e_{t−1})^2 / sum_{t=1}^n e_t^2, where e_t are the regression residuals. The value of d ranges from 0 to 4. A value near 2 suggests no first-order autocorrelation; values toward 0 indicate positive autocorrelation, while values toward 4 indicate negative autocorrelation. Critical values depend on the sample size n and the number of estimated parameters k, and are typically denoted d_L and d_U (lower and upper bounds).

Decision rules are based on these bounds: if d < d_L, there is evidence of positive autocorrelation; if d > d_U, there is evidence of negative autocorrelation; if d lies between d_L and d_U, the test is inconclusive. Because the distribution is irregular and depends on model specifics, exact p-values are not always available; practitioners often rely on tables or software.

Assumptions and limitations include correct model specification, absence of a lagged dependent variable among the regressors, and stationarity of errors. The Durbin-Watson test is most appropriate for detecting first-order autocorrelation and may be unreliable in the presence of higher-order autocorrelation or complex time-series structures; in such cases, alternatives like the Breusch-Godfrey test are used. The test was developed by James Durbin and Geoffrey Watson in the early 1950s.