# Durbin-Watson Test and p-value

What should I do if the p-value in Durbin-Watson test is zero (using R)?

Usually a hypothesis test indicates a failure to reject the null hypothesis when the p-value is 0.

The Durbin-Watson test tests for autocorrelation. However due to the particular nature of autocorrelation (positive and negative autocorrelation) there is a special test statistic: The Durbin-Watson statistic. Therefore the Durbin-Watson test has a value of the test statistic, but no p-value.

The Durbin-Watson test statistic works in the following manner:

• Test statistic value of 0: Perfect positive autocorrelation
• Test statistic value 0f 2: No autocorrelation
• Test statistic value of 4: Perfect negative autocorrelation

If your Durbin-Watson test is perfectly positive autocorrelated you should correct it in order to make the data stationary before doing further analysis.

• Thanks for your answer, but how can I correct the autocorrelation in my model? Commented May 17, 2019 at 13:09
• It should be noted that there are procedures to compute the distribution and hence a p value for the DW statistic, see Imhof (1961), Farebrother (1980, 1984). Commented May 17, 2019 at 13:30
• @Dimitris Check that out if you are using ARIMA. towardsdatascience.com/… Helix123 Thank you for this useful information. Commented May 17, 2019 at 13:36
• The standard durbin watson only test for first order autocorrelation although other tests have been developed to deal with more advanced forms of it. If you are concerned about serial correlation influencing your test then I think HAC standard errors will address this. If you want to use past lags of x and y to predict y then there are methods such as vector regressive models or ARDL that have been created to address this. None are simple IMHO. Commented May 20, 2019 at 23:56
• This is answered in various other posts, like stats.stackexchange.com/questions/153286/…, stats.stackexchange.com/questions/154167/…, stats.stackexchange.com/questions/160830/… Commented Jun 15, 2019 at 10:32