Two topics in temporal graphical probabilistic models are studied. The topics are treated in separate papers, both with applications in finance. The first 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 and some toy examples with promising results. The second paper treats probabilistic graphical models in continuous time —a class of models with the ability to express causality. Tools for inference in these models are developed and employed in the design of a causality measure. The framework is used to analyze tick-by-tick data from the foreign exchange market.
Två teman inom temporala grafiska modeller betraktas. De behandlas i separata artiklar, båda med tillämpningar inom finans. Den första artikeln studerar inferens i dynamiska Bayesianska nätverk med Monte Carlo-metoder. En ny metod för att simulera slumptal föreslås. Metoden delar upp tillståndsrummet i underrum. Detta gör att simuleringarna kan utföras parallellt med oberoende och distinkta simuleringstekniker på underrummen. Metodiken demonstreras på en volatilitesmodell och ett par leksaksmodeller med lovande resultat. Den andra artikeln behandlar probabilistiska grafiska modeller i kontinuerlig tid. Dessa modeller har förmåga att uttrycka kausalitet. Verktyg för inferens i dessa modeller utvecklas och används för att designa ett kausalitets-mått. Ramverket tillämpas genom att analysera tick-data från valutamarknaden.
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.