Autocorrelation occurs when the residuals are not independent of each other. That is, when the value of e[i+1] is not independent from e[i].
While a residual plot, or lag-1 plot allows you to visually check for autocorrelation, you can formally test the hypothesis using the Durbin-Watson test. The Durbin-Watson statistic is used to detect the presence of autocorrelation at lag 1 (or higher) in the residuals from a regression. The value of the test statistic lies between 0 and 4, small values indicate successive residuals are positively correlated. If the Durbin-Watson statistic is much less than 2, there is evidence of positive autocorrelation, if much greater than 2 evidence of negative autocorrelation.
