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Multivariate Hawkes processes: an application to financial data

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Paul Embrechts ,
Thomas Liniger  and
Lu Lin
Paul Embrechts
Affiliation:
ETH Zürich and Swiss Finance Institute, RiskLab, Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. Email address: embrechts@math.ethz.ch
Thomas Liniger
Affiliation:
ETH Zürich, Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
Lu Lin
Affiliation:
ETH Zürich, Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
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Abstract

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A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.

Keywords

Multivariate Hawkes processpoint processclusteringself-exciting

MSC classification

Primary: 60G55: Point processes
Type
Part 8. Point Processes
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 367 - 378
Copyright
Copyright © Applied Probability Trust 2011 

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