Research being undertaken by our current postgraduates:

Feb 2014

Analysis of Financial Time Series through Complex Networks

Analysis of time series data in order to infer the underlying dynamical system generating a physical process has traditionally been investigated using statistical techniques. Recently, a number of methods which treat time series in a different manner have been developed. This new approach links time series to complex networks. Network theory has been extensively studied, starting historically from graph theory in the field of pure mathematics and continuing with a rich literature in several fields, among which applied mathematics, physics, computer science, sociology and biology. Thus, if a specified time series can be represented by a corresponding complex network, various techniques and tools exist in order to examine the structural properties of the network and draw conclusions about the original time series. In this project, we are going to examine the existing transformation techniques and perhaps develop new ones. Our focus will be networks with nodes that exhibit stochastic behaviour as the deterministic case has been investigated much more widely. Inferring the properties of the general network structure from the probabilistic behaviour of its individual components will be one of the main research questions we are going to consider. The other big challenging theme of this project will be attempting to apply our theoretical work onto understanding complex financial systems, such as the stock or derivative markets' behaviour, from the existing time series data. The goals will be to infer unknown and counterintuitive facets of such systems by means of the complex network approach and to assess the short-term predictive power of our techniques in determining the future evolution of the time series, a very challenging topic in modern finance.

Our research has several important aspects in terms of the potential contribution to three big, challenging and currently very popular fields of research: analysis of nonlinear time series, complex networks and mathematical finance. In every field of study, scientists take measurements of a physical process and thereafter use the collected data to try to make inferences and obtain novel insight regarding the underlying process. The case of linear processes has been widely examined and there exist many theoretical tools towards the analysis of their time series. However, the vast majority of natural phenomena fall under the umbrella of the nonlinear case, which is much more challenging mathematically and the existing literature is much more incomplete in comparison. Various fields require more advanced knowledge of time series analysis, and none more than the constantly developing field of mathematical finance. Mathematical models in modern finance, especially portfolio management and asset pricing, have historically had numerous limitations ever since the emergence of the field from that seminal paper by Harry Markowitz [1952]. Time series data and theoretical models share a unique relationship of continuous feedback back and forth. Therefore, advancements in the analysis of time series will result in better understanding of the natural processes in question and, thereby, improvement of the models and the theory of modern finance. Finally, the development of complex networks theory will have several applications, not only in nonlinear time series analysis, but also in information theory, computer science and the structure of the web, engineering and the internet (referring to the physical network of wires and cables), subcellular processes in biology, the neuronal network, social networks and many other fields.

- SIRF, UIS

Assistance in statistics is available for Postgraduates students by research at the UWA Centre for Applied Statistics.