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dc.contributor.author
Kirchner, Matthias
dc.contributor.supervisor
Embrechts, Paul
dc.contributor.supervisor
Chavez-Demoulin, Valérie
dc.contributor.supervisor
Hawkes, Alan
dc.contributor.supervisor
Mikosch, Thomas
dc.date.accessioned
2019-02-27T07:53:59Z
dc.date.available
2017-06-19T11:37:41Z
dc.date.available
2017-07-04T08:50:28Z
dc.date.available
2017-07-04T09:02:36Z
dc.date.available
2017-07-05T08:11:52Z
dc.date.available
2017-08-25T12:30:40Z
dc.date.available
2017-08-25T12:43:21Z
dc.date.available
2019-02-27T07:53:59Z
dc.date.issued
2017
dc.identifier.isbn
978-3-906327-81-5
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/161487
dc.identifier.doi
10.3929/ethz-b-000161487
dc.description.abstract
This thesis addresses Hawkes point processes in seven scientific papers. We build theoretical bridges between Hawkes processes and other mathematical concepts---such as time series, branching random walks, or graph theory. In Paper A, we represent monotype Hawkes processes as limits of time-series based point processes. We examine the corresponding time series, the integer-valued autoregressive (INAR) time series of infinite order, in some detail. Furthermore, we point out structural analogies between Hawkes processes and INAR time series. In Paper B, we represent multitype Hawkes processes as type/space projections of certain branching random walks. This representation allows to generalize the convergence result from Paper A to the multitype case. Furthermore, it opens the door to generalizations of Hawkes processes that might be interesting in applications. In Paper C, we introduce a nonparametric estimation procedure for multitype Hawkes processes: we discretize Hawkes-process data. From Paper A and B, we know that the resulting bin-count sequences can be approximated by INAR time series. Thus, we estimate the INAR parameters by standard methods and retranslate the results into the point process world. In Paper D, we represent multitype Hawkes processes as directed weighted graphs. These `Hawkes graphs' summarize the branching structure of a Hawkes process in a compact, yet meaningful way. We point out how the graphical perspective is also fertile mathematically, implementation-wise, and pedagogically. Furthermore, we apply the estimation method from Paper C to infer the Hawkes graph from large datasets. We pay special attention to computational issues. In Paper E, we apply the methods and concepts from Paper C and Paper D to limit-order-book data. In particular, we extend our estimation procedure to the marked case. The various estimation results allow insights into market microstructure. In Paper F, we give the results of a simulation study, where we compare our estimation procedure with maximum-likelihood estimation. Finally, in Paper G, we consider a certain critical case of the monotype Hawkes process. We study the critical Hawkes process by applying results from critical cluster fields, renewal theory, and regular variation. We discuss a possible Poisson embedding and a Palm version of the critical Hawkes process. Our methods give possible directions for the open discussion of multitype critical Hawkes processes as well as of critical INAR times series.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.title
Perspectives on Hawkes Processes
en_US
dc.type
Doctoral Thesis
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2017-08-25
ethz.size
273 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
ethz.identifier.diss
24278
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03288 - Embrechts, Paul (emeritus)
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03288 - Embrechts, Paul (emeritus)
en_US
ethz.date.deposited
2017-06-19T11:37:41Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.date.embargoend
2019-02-28
ethz.rosetta.installDate
2017-07-05T08:12:04Z
ethz.rosetta.lastUpdated
2020-02-15T17:32:55Z
ethz.rosetta.versionExported
true
ethz.COinS
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