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Multivariable zero-free Transfer Functions and Spectra, and their application in Economic Modelling

Central banks and funds investment managers work with mathematical models. In recent years, a new class of model has come into prominenceógeneralized dynamic factor models. These are characterized by having a modest number of inputs, corresponding to key economic variables and industry-sector-wide variables for central banks and funds managers respectively, and a large number of outputs, economic time series data or individual stock price movements for example. It is common to postulate that the input variables are linked to the output variables by a finite-dimensional linear time-invariant discrete-time dynamic model, the outputs of which are corrupted by noise to yield the measured data. The key problems faced by central banks or funds managers are model fitting given the output data (but not the input data), and using the model for prediction purposes. These are essentially tasks usually considered by those practicing identification and time series modelling. Nevertheless there is considerable underlying linear system theory. This flows from the fact that the underlying transfer function matrix is tall. This presentation will describe a number of consequences of this seemingly trivial fact. For example, a tall transfer function of known McMillan degree but otherwise generic has no zeros, finite or infinite. A finite sequence of output data in the discrete time case allows recovery of a finite sequence of input data, without knowledge of the initial state. Canonical autoregressive models take on a special structure, with the number of real parameters growing linearly with the number of outputs, rather than, as usual, quadratically.
Type of Seminar:
Public Seminar
Prof. Brian D.O. Anderson
Research School of Information Sciences and Engineering, The Australian National University
Jun 03, 2010   15:15

ETH Zentrum, Gloriastr. 35, Building ETZ, Room E6
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Brian Anderson took his undergraduate degrees in Mathematics and Electrical Engineering at Sydney University, and his doctoral degree in Electrical Engineering at Stanford University. He worked in industry in the United States and at Stanford University before serving as Professor of Electrical Engineering at the University of Newcastle, Australia from 1967 through 1981. At that time, he took up a post as Professor and Head of the Department of Systems Engineering at the Australian National University in Canberra, where he was Director of the Research School of Information Sciences and Engineering from 1994 to 2002. For approximately one year to May 2003, he was the inaugural CEO of the newly formed National ICT Australia, established by the Australian Government through the Department of Communications, Information Technology and the Arts and the Australian Research Council under the Information and Communication Technologies Centre of Excellence program. Professor Anderson has served as a member of a number of government bodies, including the Australian Science and Technology Council and the Prime Minister's Science, Engineering and Innovation Council. He was a member of the Board of Cochlear Limited, the world's major supplier of cochlear implants from its listing until 2005. He is a Fellow of the Australian Academy of Science and Academy of Technological Sciences and Engineering, the Institute of Electrical and Electronic Engineers, and an Honorary Fellow of the Institution of Engineers, Australia. In 1989, he became a Fellow of the Royal Society, London, and in 2002 a Foreign Associate of the US National Academy of Engineering. He holds honorary doctorates of the Catholic University of Louvain in Belgium, the Swiss Federal Institute of Technology, and the Universities of Sydney, Melbourne and New South Wales. He was appointed an Officer of the Order of Australia in 1993. He was President of the International Federation of Automatic Control for the triennium 1990 to 1993, and served as President of the Australian Academy of Science for four years from 1998 to 2002. Professor Anderson became the Chief Scientist of National ICT Australia in May 2003 and served in that role till September 2006. His current interests are in control of distributed systems and adaptive control.