Eur. Phys. J. B 78, 235-243 (2010)
https://doi.org/10.1140/epjb/e2010-10046-8

Segmentation algorithm for non-stationary compound Poisson processes

With an application to inventory time series of market members in a financial market

¹ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, 87501, USA
² Dipartimento di Fisica e Tecnologie Relative, Universitá di Palermo, 90100 Palermo, Italy
³ LUISS Guido Carli, Viale Pola 12, 00198 Roma, Italy

Corresponding author: ^a bence@santafe.edu

Received: 14 January 2010
Revised: 2 September 2010
Published online: 28 October 2010

Abstract

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 a time series. The process is composed of consecutive patches of variable length. In each patch the process is described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated with 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-Galván, et al. [Phys. Rev. Lett. 87, 168105 (2001)]. We show that the new algorithm outperforms the original one for regime switching models of 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.