报告人：Dr.Matthias Kirchner（University of Teacher Education Bern）
In this talk, we give an introduction to Hawkes processes emphasizing their autoregressive structure - the reason why Hawkes processes `always fit'. Furthermore, we study a discretization of the (multitype) Hawkes process, counting points in bins. We show that the resulting bin-count sequence may be approximated by (multivariate) integer-valued autoregressive (INAR) time series. In the INAR context, we derive asymptotically normal estimators and provide estimates of their standard deviation. Retranslating these results from the time series world into the point process world gives rise to a nonparametric estimation method for Hawkes processes. In an example on multitype limit-order-book event streams, we illustrate how this estimation method may be used to specify Hawkes models from data with few a priori assumptions. At the same time, we point out some issues that arise around the use of Hawkes processes: `Causal' interpretation, discreteness of time lines, and the impossibility of negative autocorrelation.
Dr. Matthias Kirchner is a lecturer for mathematics and music at the University of Teacher Education in Bern, Switzerland. Furthermore, he is member of the executive board of the institute IVP NMS and head of the department "applied scientific theory and subject teaching and learning". He received a Ph.D. degree in mathematics from ETH Zurich in 2017 under the supervision of Paul Embrechts. His thesis was honored with the ETH-medal and with the Walter-Saxer price. He also holds a teaching and a concerto diploma for guitar from the University of the Arts, Bern.
Matthias Kirchner is a specialist for the so called "Hawkes process" - a flexible mathematical tool to model event streams such as earthquakes, price jumps or outbreaks of diseases. As such, he is regularly invited to give talks on the topic. E.g., in the last year: Sorbonne University, Paris, the Université de Lausanne, or the CMStatistics 2018 in Pisa. Furthermore, he is a wanted referee for peer-reviewed journals. He has published in refereed journals, such as Stochastic Processes and their Applications, Quantitative Finance, Theory Of Probability and Its Applications and Journal of Statistical Computation and Simulation. Citations show that his work receives considerable attention. His research has been supported by the Swiss Finance Institute. He is member of the Swiss Statistical Society.