Correlated random variables with additional autocorrelation - multi dimensional Cholesky?

For my thesis I'm currently generating several time series of random numbers, so far so good. Now I realized some autocorrelation in the series as well and don't really know how to cope with it. Can I use the Cholesky factorization to generate random numbers with auto-correlation and then afterwards use the Cholesky decomposition again for simulating with the overall correlation structure between the different time series? Because I'm uncertain whether that destroys the autocorrelation I previously created?

Or put differently, I'm currently doing this for $n$ variables:

$$x_{t,1} = x_{t,0} \exp(my+std\cdot rv_1)$$ $$y_{t,1} = y_{t,0} \exp(my+std(p\cdot rv_1+(1-p^2)^{0.5}rv_2))$$

Now those are correlated just fine, but how do I insert the autocorrelation without harming the cross series correlation? Or is it unaffected when I change the random variables?