Segmentation algorithm for non-stationary compound Poisson processes

We introduce an algorithm for the segmentation of a class of regime switching
processes. The segmentation algorithm is a non parametric statistical method
able to identify the regimes (patches) of the time series. The process is
composed of consecutive patches of variable length, each patch being described
by a stationary compound Poisson process, i.e. a Poisson process where each
count is associated to a fluctuating signal. The parameters of the process are
different in each patch and therefore the time series is non stationary. Our
method is a generalization of the algorithm introduced by Bernaola-Galvan, et
al., Phys. Rev. Lett., 87, 168105 (2001). We show that the new algorithm
outperforms the original one for regime switching compound Poisson processes.
As an application we use the algorithm to segment the time series of the
inventory of market members of the London Stock Exchange and we observe that
our method finds almost three times more patches than the original one.