# Augmented Dickey-Fuller test - showing residuals are serially uncorrelated

I ran an Augmented Dicket-Fuller test to see if there was a unit root present in my time series. I would know like to show that the residuals from the test regression are serially uncorrelated. In the output there is the Durbin-Watson statistic - is this value enough to show the uncorrelation? Or is there a better way?

No, the Dickey-Fuller test statistic does not show whether the residuals are serially correlated. To find that out, you should either

1. manually build the test regression and extract the residuals; or
2. extract the residuals from the output of the Dickey-Fuller test;

and then test them for autocorrelation. Breusch-Godfrey test can be used for that (but it requires a whole model, not only the residuals). Here is how you can do it in R using "lmtest" and "urca" packages:

library(lmtest)
library(urca)
bgtest(ur.df(x))


where x is your time series.

• Thanks for your response Richard. I have added a snag of an example of an ADF regression. Could you please explain what the Durbin-Watson stat means in this example? I thought that because it was close to 2 it implies the residuals are not correlated? Or am I not understanding it correctly? – user156352 May 13 '17 at 11:18
• @EconometricsHelp, Durbin-Watson tests for autocorrelation at lag 1. It indeed shows there is hardly any autocorrelation at lag 1. But you should also look for autocorrelation at higher lags, and that can be done by the Breusch-Godfrey.test, for example. – Richard Hardy May 13 '17 at 19:24
• @EconometricsHelp, is it clear now, or do you need some further clarification? I see you have neither accepted nor upvoted the answer. – Richard Hardy Jun 16 '17 at 13:24