  We discuss intermittent time series consisting of discrete bursts or
avalanches separated by waiting or silent times. The short time correlations
can be understood to follow from the properties of individual avalanches, while
longer time correlations often present in such signals reflect correlations
between triggerings of different avalanches. As one possible source of the
latter kind of correlations in experimental time series, we consider the effect
of a finite detection threshold, due to e.g. experimental noise that needs to
be removed. To this end, we study a simple toy model of an avalanche, a random
walk returning to the origin or a Brownian bridge, in the presence and absence
of superimposed delta-correlated noise. We discuss the properties after
thresholding of artificial timeseries obtained by mixing toy avalanches and
waiting times from a Poisson process. Most of the resulting scalings for
individual avalanches and the composite timeseries can be understood via random
walk theory, except for the waiting time distributions when strong additional
noise is added. Then, to compare with a more complicated case we study the
Manna sandpile model of self-organized criticality, where some further
complications appear.
