Which test for autocorrelation in a time series

I need your help to test autocorrelation between residuals of a time series. But I don't know which test use: Breusch Godfrey test, ARCH test or Durbin–Watson test.. I don't understand the difference between those tests. Anyone has a suggestion?

And my other question is: I already know there are heteroscedasticity and if there are autocorrelation too, how can I estimate my coefficients? Which method can I use?

Thank you in advance! Greg

• Have you at least checked the Wikipedia sites for these tests? The one for Breush-Godfrey (BG) includes a comparison of BG to Durbin-Watson (DW) and explains why BG is preferred among the two. ARCH-LM test is for conditional heteroskedasticity which is a different thing than autocorrelation. Regarding your second question, consider using ARIMA-GARCH models which account for both autocorrelation and conditional heteroskedasticity. If you have more than one variable in the model, consider using regression with ARIMA-GARCH errors. Function ugarschspec in "rugarch" package in R may be useful. – Richard Hardy Mar 2 '16 at 7:35
• Yes, I already checked but I don't understand how you can have nonstochastic regressors. But I gonna use BG test! For my second question, do you think I can use the Newey-West estimators too? Thanks – tssssddde Mar 2 '16 at 11:05
• Yes, Newey-West could be an alternative. It provides half a remedy; it does not fix the point estimates but expands the confidence intervals to account for the violation of i.i.d.'ness of residuals. Meanwhile, explicit ARMA-GARCH modelling provides a full remedy; it fixes point estimates and does not expand the confidence intervals. – Richard Hardy Mar 2 '16 at 12:09
• Is it possible to find homoskedasticity and autocorrelation for the same model? – tssssddde Mar 2 '16 at 14:52
• Generally, yes. – Richard Hardy Mar 2 '16 at 16:23