Fractional Integration, Power Laws and Econometric Models: Some Methodological and Theoretical Developments. The fundamental objectives of this project are to: (i) Extend
current econometric practice and consider the use of power laws as
a basis for the construction of a more flexible and realistic
class of models for the analysis of economic and financial time
series. (ii) To develop inferential techniques appropriate for the
modelling of dynamic econometric systems that incorporate
struc ....Fractional Integration, Power Laws and Econometric Models: Some Methodological and Theoretical Developments. The fundamental objectives of this project are to: (i) Extend
current econometric practice and consider the use of power laws as
a basis for the construction of a more flexible and realistic
class of models for the analysis of economic and financial time
series. (ii) To develop inferential techniques appropriate for the
modelling of dynamic econometric systems that incorporate
structure characterized by power laws. This will be achieved by
building upon the class of fractionally integrated processes. New
econometric models and methodologies for the analysis of
non-stationarity series will be developed, along with the
associated theoretical results.Read moreRead less
Forecasting with single source of randomness state space models. The framework developed in this project, for identifying and
extrapolating trends, seasonal patterns and economic cycles in time
series, has a large and diverse range of useful applications in
Australia. Some examples include its potential use in the
development of appropriate monetary policy, its use to better inform
finance markets of risk levels associated with shares, its use to
forecast demand in supply chains to provide ....Forecasting with single source of randomness state space models. The framework developed in this project, for identifying and
extrapolating trends, seasonal patterns and economic cycles in time
series, has a large and diverse range of useful applications in
Australia. Some examples include its potential use in the
development of appropriate monetary policy, its use to better inform
finance markets of risk levels associated with shares, its use to
forecast demand in supply chains to provide a better service to
customers, and its use in call centres to better tailor staff
schedules to meet customer calls.Read moreRead less
Filled function methods for global optimization and their applications. Many real problems in science, commerce and industry are restricted in the way that they are modelled and solved by the known inability to deal with global optimization problems. The development of computational efficient global optimization methods in this project will allow new more complete approaches to these problems, especially in new areas of bio-informatics, data mining, economic modelling, supply chain management, ....Filled function methods for global optimization and their applications. Many real problems in science, commerce and industry are restricted in the way that they are modelled and solved by the known inability to deal with global optimization problems. The development of computational efficient global optimization methods in this project will allow new more complete approaches to these problems, especially in new areas of bio-informatics, data mining, economic modelling, supply chain management, air traffic management, biochemical engineering and automotive industry, consequently helping Australia advance in these various areas. It will also enhance the understanding of global optimization from both theoretical and numerical viewpoints, particularly boosting optimization research in Australia.Read moreRead less
Duality, singular perturbations and numerical analysis in infinite dimensional linear programming problems related to problems of control of nonlinear dynamical systems. Problems of control of nonlinear dynamical systems attract continued interest of eminent researchers motivated by important applications and by the fact that analytical and/or numerical analysis of a general nonlinear control problem presents a challenging task. The outcomes of the project will be both fundamental theoretical re ....Duality, singular perturbations and numerical analysis in infinite dimensional linear programming problems related to problems of control of nonlinear dynamical systems. Problems of control of nonlinear dynamical systems attract continued interest of eminent researchers motivated by important applications and by the fact that analytical and/or numerical analysis of a general nonlinear control problem presents a challenging task. The outcomes of the project will be both fundamental theoretical results and readily applicable (linear programming based) algorithms that will equip researchers and engineers with new tools for analysis and numerical solution of nonlinear control problems (including problems that have been intractable so far). The project will further enhance Australia's international reputation in Control Theory and its Applications.
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New approaches to the statistical modelling of financial risk: combining structural information with flexible, computationally-intensive non-parametric methods. The aims of this project are to provide a range of novel, rigorous, flexible, statistical methods to assess portfolio risk, with due attention to behaviour of its constituent components; to obtain greater understanding of the complexities of risk; and to give students research training in the nexus of statistics and finance. The anticip ....New approaches to the statistical modelling of financial risk: combining structural information with flexible, computationally-intensive non-parametric methods. The aims of this project are to provide a range of novel, rigorous, flexible, statistical methods to assess portfolio risk, with due attention to behaviour of its constituent components; to obtain greater understanding of the complexities of risk; and to give students research training in the nexus of statistics and finance. The anticipated outcomes of this project will be detailed knowledge of extremal behaviour in portfolios, improved methods for calibrating risk, advances in non-parametric methods in finance, a prototype practitioner toolkit for assessing risk, and high-calibre graduates to contribute to Australia's research capacity.Read moreRead less
Occupational Measures Approach to Long Run Average and Singularly Perturbed Optimal Control Problems. Problems of optimal control of long-run average and singularly perturbed systems arise in many applications. The project will lead to the development of new linear programming based techniques for analyzing these problems (including problems intractable so far) and finding their numerical solutions. The new techniques will have a potential to be further developed into software that can benefit A ....Occupational Measures Approach to Long Run Average and Singularly Perturbed Optimal Control Problems. Problems of optimal control of long-run average and singularly perturbed systems arise in many applications. The project will lead to the development of new linear programming based techniques for analyzing these problems (including problems intractable so far) and finding their numerical solutions. The new techniques will have a potential to be further developed into software that can benefit Australian industries and technologies. The proposed topic is in the focus of interest of many eminent researchers around the world and the dissemination of our results will further improve Australia's standing in the international research community. Read moreRead less
Operations research without convexity. Operations Research (OR) is one of the most applicable areas of mathematics and of importance for the future of technologically advanced Australia. However, applications of OR often require convexity. This is a serious limitation. A new approach, monotonic analysis, which is applicable to a broad class of nonconvex problems, was given birth by the CI. Promising results have been obtained and leading researchers around the world (including the Presidents ....Operations research without convexity. Operations Research (OR) is one of the most applicable areas of mathematics and of importance for the future of technologically advanced Australia. However, applications of OR often require convexity. This is a serious limitation. A new approach, monotonic analysis, which is applicable to a broad class of nonconvex problems, was given birth by the CI. Promising results have been obtained and leading researchers around the world (including the Presidents of the Canadian Mathematical and French Applied Mathematics Societies) are keen to work with the CI developing this topic. This project both cements and extends world leadership in this field.Read moreRead less
Modelling the Choices of Individuals. Individuals make decisions daily and some of these decisions have wide-reaching and long-term consequences, such as choices among housing, public transport, electoral candidates and health care options. The principal aim of this project is to develop reliable and valid ways to model individual level choice processes. Once completed, this will provide insights into ways to aggregate sampled observations when population-level applications are required, and all ....Modelling the Choices of Individuals. Individuals make decisions daily and some of these decisions have wide-reaching and long-term consequences, such as choices among housing, public transport, electoral candidates and health care options. The principal aim of this project is to develop reliable and valid ways to model individual level choice processes. Once completed, this will provide insights into ways to aggregate sampled observations when population-level applications are required, and allow us to compare and test several competing theories of choice behaviour. This will enable us to make contributions to understanding and modelling human decision making in many fields ranging from marketing to medicine.Read moreRead less
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