# statsmodels.stats.stattools.durbin_watson¶

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

Calculates the Durbin-Watson statistic

Parameters

resids (array-like) –

Returns

dw – The Durbin-Watson statistic.

Return type

float, array-like

Notes

The null hypothesis of the test is that there is no serial correlation. The Durbin-Watson test statistics 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.