New Robust Identification Method for Controlled Hawkes Processes
Michael Mark and Prof. Thomas Weber’s recent research on “Robust Identification of Controlled Hawkes Processes,” published in the Physical Review E of the American Physical Society, introduces a new method to estimate controlled self-exciting point processes. This class of processes has many applications, for example, in credit collections, financial markets, advertising, social networks, and—traditionally—earthquake prediction. The main idea is to leverage the internal branching representation of the process. The convergence properties of the method are significantly better than what can be achieved with traditional maximum-likelihood estimation methods.
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.
Mark, M., Weber, T.A. (2020) “Robust Identification of Controlled Hawkes Processes,” Physical Review E, Vol. 101, No. 4, Article 043305. [DOI: 10.1103/PhysRevE.101.043305; open access]