How can I test if a not independently and not identically distributed time series residuals' are uncorrelated ?

Ok I made Jarque-Bera test to the residuals (merv.reg$residual)

library(tseries)
jarque.bera.test(merv.reg$residual)
X-squared = 1772.369, df = 2, p-value = < 2.2e-16
And I reject the null hypotesis (H0: merv.reg$residual are normally
distributed)

So I know that:
1 - merv.reg$residual aren't independently distributed (Box-Ljung test)
2 - merv.reg$residual aren't indentically distributed (Breusch-Pagan test)
3 - merv.reg$residual aren't normally distributed (Jarque-Bera test)

My questions is:
It is possible merv.reg$residual   be uncorrelated ?
cov[residual_t, residual_(t+k)] = 0 ?
Even when residuals  are not independent distributed !
(and we know that they aren't normally distributed and they aren't
indentically distributed )
And how can I tested it ?

Thanks.

Hint, if a ts is normally distributed then independence and

uncorrelatedness

are equivalent, hence you can test for normally distributed errors (e.g.
Jarque-Bera-Test).

HTH,
Bernhard