Further details and publications on these topics can be seen in the Research Interests section
Chaos Communication Modelling
This talk will deal with the communications-engineering research area of chaos-based communications systems - systems in which message bits are carried and spread by discrete-time chaotic waves rather than periodic waves. Such systems have potential for security, capacity and resistance to interference. Development of the area heavily depends on the statistical and dynamical aspects of chaotic processes and their interplay with channel stochastic noise and interference. While the area is a very active one in several groups of international and mathematically educated electronics researchers, it faces some challenges which are most suitably approached with mathematical and statistical expertise. The main theoretical aspects are those of bit estimation and bit error, both highly statistical. Previous engineering approaches ignored some key points and gave unsatisfactory approximations. Work on the chaos-shift keying system by the speaker and collaborators has produced exact results which give considerable insight of engineering value. Latest work involves develeopments to laser-based shift-keying communications systems and the analysis of very long sequences of data collected over very short time periods. Chaos-based communications is one area in nonlinear engineering where statisticians can make a difference.
This topic can be covered at an introductory level for statistical audiences or at a level which assumes knowledge of the area and which goes more into current issues and advances.
Statistical Analysis in Financial Time Series
This topic being developed is concerned with the graphics and modelling of volatility in time series. A general modelling basis for stationary time series allowing changing level and volatility is used to suggest graphics which explore the existence of volatility, its dependence on earlier values in the time series, and possible ways in which it depends on earlier values. The importance of prior decorrelation is explored. Illustrations use financial series, while simulations are employed for validation purposes. The well-known signature of volatility, the clustering of oppositely signed extremes, is captured by the plot of their squared deautocorrelated values and its autocorrelations. This prompts investigating the explicit model of squared values when the unsquared deautocorrelated values follow garch models. In fact, the squared values follow arma models except that their innovations are themselves garch-like volatile and dependent, as seen in examples from financial series. A final point concerns the usefulness of linear dependency in financial series, however slight, and motivates modifying the iconic arch and garch volatility models to include linear dependence in a natural way suggested by the previous volatility developments.