  A sequence of bursts observed in an intermittent time series may be caused by
a single avalanche, even though these bursts appear as distinct events when
noise and/or instrument resolution impose a detection threshold. In the
Bak-Tang-Wiesenfeld sandpile, the statistics of quiet times between bursts
switches from Poissonian to scale invariant on raising the threshold for
detecting instantaneous activity, since each zero-threshold avalanche breaks
into a hierarchy of correlated bursts. Calibrating the model with the time
resolution of GOES data, qualitative agreement with the inter-occurrence time
statistics of solar flares at different intensity thresholds is found.
