  We demonstrate that continuous time random walks in which successive waiting
times are correlated by Gaussian statistics lead to anomalous diffusion with
mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the
waiting times with power-law exponent alpha (0<alpha<=2) give rise to
subdiffusion of the form <r^2(t)>~t^{alpha/(1+alpha)}. In contrast correlations
in the jump lengths are shown to produce superdiffusion. We show that in both
cases weak ergodicity breaking occurs. Our results are in excellent agreement
with simulations.
