  Time series resulting from wave decomposition show the existence of different
correlation patterns for avalanche dynamics. For the d=2 Bak-Tang-Wiesenfeld
model, long range correlations determine a modification of the wave size
distribution under coarse graining in time, and multifractal scaling for
avalanches. In the Manna model, the distribution of avalanches coincides with
that of waves, which are uncorrelated and obey finite size scaling, a result
expected also for the d=3 Bak et al. model.
