statsmodels.stats.stattools.durbin_watson¶

statsmodels.stats.stattools.durbin_watson(resids, axis=0)[source]¶

Calculates the Durbin-Watson statistic.

Parameters:¶

residsarray_like

Data for which to compute the Durbin-Watson statistic. Usually regression model residuals.

axisint, optional

Axis to use if data has more than 1 dimension. Default is 0.

Returns:¶

dwfloat, array_like

The Durbin-Watson statistic.

Notes

The null hypothesis of the test is that there is no serial correlation in the residuals. The Durbin-Watson test statistic is defined as:

\[\sum_{t=2}^T((e_t - e_{t-1})^2)/\sum_{t=1}^Te_t^2\]

The test statistic is approximately equal to 2*(1-r) where r is the sample autocorrelation of the residuals. Thus, for r == 0, indicating no serial correlation, the test statistic equals 2. This statistic will always be between 0 and 4. The closer to 0 the statistic, the more evidence for positive serial correlation. The closer to 4, the more evidence for negative serial correlation.