Robust Identification of Controlled Hawkes Processes

Physical Review E, Vol. 101, No. 4 (April 2020), Article 043305

16 Pages Posted: 14 Mar 2020 Last revised: 21 Apr 2020

See all articles by Michael Mark

Michael Mark

Ecole Polytechnique Federale de Lausanne

Thomas A. Weber

Ecole Polytechnique Federale de Lausanne - MTEI

Date Written: February 20, 2020

Abstract

The identification of Hawkes-like processes can pose significant challenges. Despite substantial amounts of data, standard estimation methods show significant bias or fail to converge. To overcome these issues, we propose an alternative approach based on an expectation-maximization algorithm, which instrumentalizes the internal branching-structure of the process, thus improving convergence behavior. Furthermore, we show that our method provides a tight lower-bound for maximum-likelihood estimates. The approach is discussed in the context of a practical application, namely the collection of outstanding unsecured consumer debt.

Keywords: Controlled self-exciting point processes, expectation maximization, Hawkes processes, maximum-likelihood estimation, robust identification

JEL Classification: C13, C22, C51, G21, G32

Suggested Citation

Mark, Michael and Weber, Thomas A., Robust Identification of Controlled Hawkes Processes (February 20, 2020). Physical Review E, Vol. 101, No. 4 (April 2020), Article 043305, Available at SSRN: https://ssrn.com/abstract=3470174

Michael Mark (Contact Author)

Ecole Polytechnique Federale de Lausanne ( email )

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1015 Lausanne, CH-1015
Switzerland

Thomas A. Weber

Ecole Polytechnique Federale de Lausanne - MTEI ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland
+41 (0)21 693 01 41 (Phone)
+41 (0)21 693 00 20 (Fax)

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