  A continuously measured quantum system with multiple jump channels gives rise
to a stochastic process described by random jump times and random emitted
symbols, representing each jump channel. While much is known about the waiting
time distributions, very little is known about the statistics of the emitted
symbols. In this letter we fill in this gap. First, we provide a full
characterization of the resulting stochastic process, including efficient ways
of simulating it, as well as determining the underlying memory structure.
Second, we show how to unveil patterns in the stochastic evolution: Some
systems support closed patterns, wherein the evolution runs over a finite set
of states, or at least recurring states. But even if neither is possible, we
show that one may still cluster the states approximately, based on their
ability to predict future outcomes. We illustrate these ideas by studying
transport through a boundary-driven one-dimensional XY spin chain.
