Which type of residuals to use for the Durbin-Watson test (autocorrelation) I want to check if there is residual autocorrelation in my model and the test for this is the Durbin-Watson test.
I am using R and my question is if it makes a difference which type of residuals one uses when applying the test, since there are several types of residuals like deviance, pearson, working...
 A: Yes, it does. The DW test requires the full set of classical linear model assumptions, even including normality of the error terms. Hence, other types of residuals coming for instance from GLMs are not allowed.
At any rate, there are better tests for autocorrelation.
A: Be careful that the Durbin-Watson statistic is only valid for autocorrelation of order one and models without lagged dependent as explanatory variable.
If you include the lagged dependent as explanatory variable, the test will be biased towards "no-rejection of H0=no-autocorrelation" so that you may wrongly conclude about the absence of autocorrelation when in reality it suffers from such problem.
The usual Durbin-Watson statistic is: $d=\Sigma_{t=2}^T(e_t-e_{t-1})^2/\Sigma_{t=1}^Te^2_t$
The alternative test is:$h=(1-d/2)*\sqrt{T/(1-T*Var(\hat{\beta_1)})}$ where $Var(\hat{\beta_1)})$ is the estimated variance of the regression coefficient of the lagged dependent variable and $d$ is the DW statistic.
The alternative test is distributed as a Chi-squared with degrees of freedom equal to the number of explanatory variables.
You can see that if a high autocorrelation coefficient of the lagged dependent makes the null hypothesis more easily rejected. 
