Investigation of Causality Pattern Structure for the Exploration of Dynamic Time-Varying Behaviour

The analysis of time-varying interactions within multivariate systems has seen a great deal of interest within the last decade, with the international oil market being an archetypal and important system that demonstrates this behaviour. However, unlike work on static systems, research on time-varying systems rarely leverages specific information on the inter-system interactions for understanding the systems temporal dynamics. This thesis utilises this information to present methodologies for new descriptions of these systems, focussing on the international oil market. This is achieved via three experiments. The first experiment expands upon the state-of-the-art methodologies for investigating these systems; complex networks. Presenting a novel complex network approach that encodes the transitional behaviour of the dynamic interactions. The work introduces: two transition metrics, a complex network, and various metrics and properties of this network. Using this approach it is shown that for the international oil market the evolution favours staying in similar causality patterns before switching to a new group of similar patterns. The second experiment puts forth two novel paradigms for the evolution of a dynamic multivariate system, and from these paradigms the principle features that drive the systems dynamics. It is also shown demonstrated that a p-value representation of causality can improve the description of the dynamics. Through dimensional reduction based on these paradigms and prediction of the systems future states on the reduced system, that the international oil market dynamics are well captured by the total change in causality of the system. The third experiment further explores and validates a hypothesis of the international oil markets dynamics based on the findings of the first two experiments. Proposing a approach for the formal definition of such system dynamics, and applying this to the proposed hypothesis. This hypothesis is then validated via a novel clustering approaches to determine that the international oil markets state is primarily contained within clusters that slightly vary around central causality patterns, and that the system does not follow a repeated gradual change when transitioning between these clusters. This work allows for a more detailed and alternative description of a system's dynamic behaviour than those given by other current methodologies