  We show that correlated dynamics and long time memory persist in
self-organized criticality (SOC) systems even when forced away from the defined
critical point that exists at vanishing drive strength. These temporal
correlations are found for all levels of external forcing as long as the system
is not overdriven. They arise from the same physical mechanism that produces
the temporal correlations found at the vanishing drive limit, namely the memory
of past events stored in the system profile. The existence of these
correlations contradicts the notion that a SOC time series is simply a random
superposition of events with sizes distributed as a power law, as has been
suggested by previous studies.
