Non-commutative Fractal Geometry: New Invariants. This project capitilises on Australian strengths in mathematics, particularly non-commutative and fractal geometry. It will maintain and extend Australia's prominence in these subjects, providing excellent training and opportunities for young researchers. Given the wide range of applications of fractals, there is potential for future technological spin offs for Australia.
Inference in partially non-stationary time series models. Economic theories typically specify the long-run relationship between economic variables. However, researchers usually examine the long-run features of the data by fitting a restrictive class of models using criteria that have only proven useful for short-term forecasting. In this project we consider alternative models and modelling strategies that are appropriate for the study of the long-run. We also develop computer intensive (bootstra ....Inference in partially non-stationary time series models. Economic theories typically specify the long-run relationship between economic variables. However, researchers usually examine the long-run features of the data by fitting a restrictive class of models using criteria that have only proven useful for short-term forecasting. In this project we consider alternative models and modelling strategies that are appropriate for the study of the long-run. We also develop computer intensive (bootstrap) methods, which will provide a much-needed improvement over the existing (asymptotic) methods for making inference about the long-run. Our research will lead to more reliable models for long-term planning in business, industry and government.Read moreRead less
Vector ARMA Models and Macroeconomic Modelling: Some New Methodology and Algorithms. Economic variables are strongly related to each other, as well as being strongly related to their recent history. As a result, good dynamic multivariate models are crucial for effective policy making and forecasting in areas of vital national importance such as monetary and fiscal policy, environmental policy and tourism. Our project advances the frontiers of knowledge in multivariate time series modelling. The ....Vector ARMA Models and Macroeconomic Modelling: Some New Methodology and Algorithms. Economic variables are strongly related to each other, as well as being strongly related to their recent history. As a result, good dynamic multivariate models are crucial for effective policy making and forecasting in areas of vital national importance such as monetary and fiscal policy, environmental policy and tourism. Our project advances the frontiers of knowledge in multivariate time series modelling. The outcome of this project will be immediately useful for macroeconomic policy makers such as the Reserve Bank of Australia and the Treasury, and for industry bodies such as Tourism Australia. Read moreRead less
Integrated Photonics for Secure Communication and Related Applications in Financial Transaction Data Analysis. The project includes excellent basic science, semiconductor device fabrication and applied mathematics with explicitly identified consequences for innovation. There is strong potential for national economic benefits through the manufacture of new integrated photonic devices, the application of these devices in secure communication systems, the research of advanced non-linear analysis pr ....Integrated Photonics for Secure Communication and Related Applications in Financial Transaction Data Analysis. The project includes excellent basic science, semiconductor device fabrication and applied mathematics with explicitly identified consequences for innovation. There is strong potential for national economic benefits through the manufacture of new integrated photonic devices, the application of these devices in secure communication systems, the research of advanced non-linear analysis protocols, and the implementation of these in financial transaction analysis. Professional development and research education of postgraduate students and early career researchers will be carried out in a multi-disciplinary research environment with ongoing uptake of the research in industry and commercial sectors.Read moreRead less