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Structure Learning and Mixed Radix representation in Continuous Time Bayesian Networks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-6684-8088
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Continuous time Bayesian Networks (CTBNs) are graphical representations of the dependence structures between continuous time random processes with finite state spaces. We propose a method for learning the structure of the CTBNs using a causality measure based on Kullback-Leibler divergence. We introduce the causality matrix can be seen as a generalized version of the covariance matrix. We give a mixed radix representation of the process that much facilitates the learning and simulation. A new graphical model for tick-by-tick financial data is proposed and estimated. Our approach indicates encouraging results on both the tick-data and on a simulated example.

Keyword [en]
Continuous time Bayesian networks; Composable Markov Process; Graphical models; Mixed Radix; Integrated Information Theory; Causality; High-frequency data.
National Category
Probability Theory and Statistics
Research subject
Economics; Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-193926OAI: oai:DiVA.org:kth-193926DiVA: diva2:1034595
Funder
Swedish Research Council, 2009-5834
Note

QC 20161013

Available from: 2016-10-12 Created: 2016-10-12 Last updated: 2016-10-13Bibliographically approved
In thesis
1. Inference in Temporal Graphical Models
Open this publication in new window or tab >>Inference in Temporal Graphical Models
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis develops mathematical tools used to model and forecast different economic phenomena. The primary starting point is the temporal graphical model. Four main topics, all with applications in finance, are studied.

The first two papers develop inference methods for networks of continuous time Markov processes, so called Continuous Time Bayesian Networks. Methodology for learning the structure of the network and for doing inference and simulation is developed. Further, models are developed for high frequency foreign exchange data.

The third paper models growth of gross domestic product (GDP) which is observed at a very low frequency. This application is special and has several difficulties which are dealt with in a novel way using a framework developed in the paper. The framework is motivated using a temporal graphical model. The method is evaluated on US GDP growth with good results.

The fourth paper study inference in dynamic Bayesian networks using Monte Carlo methods. A new method for sampling random variables is proposed. The method divides the sample space into subspaces. This allows the sampling to be done in parallel with independent and distinct sampling methods on the subspaces. The methodology is demonstrated on a volatility model for stock prices and some toy examples with promising results.

The fifth paper develops an algorithm for learning the full distribution in a harness race, a ranked event. It is demonstrated that the proposed methodology outperforms logistic regression which is the main competitor. It also outperforms the market odds in terms of accuracy.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2016. 16 p.
Series
TRITA-MAT-A, 2016:08
National Category
Probability Theory and Statistics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-193934 (URN)978-91-7729-115-2 (ISBN)
Public defence
2016-10-21, F3, Lindstedtsvagen, Stockholm, 13:00
Opponent
Supervisors
Note

QC 20161013

Available from: 2016-10-13 Created: 2016-10-12 Last updated: 2016-10-13Bibliographically approved

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Citation style
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