Autocorrelation in standardized residuals with GARCH

[The9mm]

Hello,
i am having a little bit of trouble with my econometrics homework at the moment. I have data for the returns of the Dow Jones, which are without serial correlation when i check the residuals of a standard regression on a constant c. But after testing for ARCH-effects and fitting an appropriate GARCH(1,1)-Model the squared standardized residuals are uncorrelated, but the standardized residuals are correlated according to the Q-statistics and p-values.
Do i need to include an AR-Term in my mean equation to correct for this autocorrelation?

edit:
I am using EViews 7.