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Inference in Temporal Graphical Models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-6684-8088
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: urn:nbn:se:kth:diva-193934ISBN: 978-91-7729-115-2OAI: oai:DiVA.org:kth-193934DiVA: diva2:1034699
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
List of papers
1. Testing for Causality in Continuous time Bayesian Network Models of High-Frequency Data
Open this publication in new window or tab >>Testing for Causality in Continuous time Bayesian Network Models of High-Frequency Data
(English)Manuscript (preprint) (Other academic)
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-159953 (URN)
Note

QS 2015

Available from: 2015-02-12 Created: 2015-02-12 Last updated: 2016-10-13Bibliographically approved
2. Structure Learning and Mixed Radix representation in Continuous Time Bayesian Networks
Open this publication in new window or tab >>Structure Learning and Mixed Radix representation in Continuous Time Bayesian Networks
(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
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:nbn:se:kth:diva-193926 (URN)
Funder
Swedish Research Council, 2009-5834
Note

QC 20161013

Available from: 2016-10-12 Created: 2016-10-12 Last updated: 2016-10-13Bibliographically approved
3. Nowcasting with dynamic masking
Open this publication in new window or tab >>Nowcasting with dynamic masking
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Nowcasting consists of tracking GDP by focusing on the data flow consisting oftimely available releases. The essential features of a nowcasting data set are differing sampling frequencies, and the ragged-edge: the differing patterns of missing observations at the end of the sample due to non-synchronicity of data publications. Various econometric frameworks have been proposed to deal withthese characteristics. During a sequence of subsequent nowcast occasions, the models are traditionally re-estimated, or updated, based on an expanding dataset as more and more data becomes available. This paper proposes to take the ragged-edge structure into account when estimating a nowcast model. Instead of using all available historical data, it is here proposed to first mask the historical data so as to reflect the pattern of data availability at the specific nowcast occasion. Since each nowcast occasion exhibits its own specific ragged-edge structure, we propose to re-estimate or recalibrate the model at each juncture employing the accompanying mask, hence dynamic masking.Dynamic masking thus tailors the model to the specific nowcast occasion. It is shown how tailoring improves precision by employing ridge regressions with and without masking in a real-time nowcasting back-test.

The masking approach is motivated by theory and demonstrated on real data. It surpasses the dynamic factor model in backtests. Dynamic masking gives ease of implementation, a solid theoretical foundation, flexibility in modeling, and encouraging results; we therefore consider it a relevant addition to the nowcasting methodology.

Keyword
Nowcasting; Time-series; Masking; Ragged edge; Machine Learning.
National Category
Probability Theory and Statistics
Research subject
Economics
Identifiers
urn:nbn:se:kth:diva-193923 (URN)
Funder
Swedish Research Council, 2009-5834
Note

QC 20161013

Available from: 2016-10-12 Created: 2016-10-12 Last updated: 2016-10-13Bibliographically approved
4. Decomposition Sampling Applied to Parallelization of Metropolis-Hastings
Open this publication in new window or tab >>Decomposition Sampling Applied to Parallelization of Metropolis-Hastings
(English)Manuscript (preprint) (Other academic)
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-159952 (URN)
Note

QS 2015

Available from: 2015-02-12 Created: 2015-02-12 Last updated: 2016-10-13Bibliographically approved
5. Forecasting Ranking in Harness Racing using Probabilities Induced by Expected Positions
Open this publication in new window or tab >>Forecasting Ranking in Harness Racing using Probabilities Induced by Expected Positions
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Ranked events are pivotal in many important AI-applications such as QuestionAnswering and recommendations systems. This paper studies ranked events in the setting of harness racing.

For each horse there exists a probability distribution over its possible rankings. In the paper it is shown that a set of expected positions (and more generally, higher moments) for the horses induces this probability distribution.

The main contribution of the paper is a method which extracts this induced probability distribution from a set of expected positions. An algorithm isproposed where the extraction of the induced distribution is given by the estimated expectations. MATLAB code is provided for the methodology.

This approach gives freedom to model the horses in many different ways without the restrictions imposed by for instance logistic regression. To illustrate this point, we employ a neural network and ordinary ridge regression.

The method is applied to predicting the distribution of the finishing positions for horses in harness racing. It outperforms both multinomial logistic regression and the market odds.

The ease of use combined with fine results from the suggested approach constitutes a relevant addition to the increasingly important field of ranked events.

Keyword
Harness racing; Competitive events; Ranked expectation; Ranking; Multinomial logistic regression; Machine Learning.
National Category
Probability Theory and Statistics
Research subject
Economics; Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-193925 (URN)
Funder
Swedish Research Council, 2009-5834
Note

QC 20161013

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

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