What test can be used for heteroskedasticity and autocorrelation if it is a Random Effect model?

Hello everyone,
I have used Hausman test and got the result that I should use RE instead of FE.
And I have learned how to test heteroskedasticity for FE, by using xttest3. Though I don't know what test can be used for a RE model.
So, do you have any suggestion about how to test heteroskedasticity and autocorrelation for a RE model?

Thanks!