Einladung zum Vortrag im Kolloquium
Multivariable zero-free Transfer Functions and Spectra, and their application in Econometric Modelling
Prof. Brian Anderson
Research School of Information Sciences and Engineering
ANU College of Engineering and Computer Science
Australian National University
Dienstag, 08. Juni 2010 ˇ 16:00 Uhr
IST-Seminarraum 3.243 ˇ Pfaffenwaldring 9 ˇ Campus Stuttgart-Vaihingen
Central banks and funds investment managers work with mathematical models. In recent years, a new class of model has come into prominence—generalized 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 then 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.
Brian Anderson was born in Sydney, Australia, and received his undergraduate education at the University of Sydney, with majors in pure mathematics and electrical engineering. He subsequently obtained a PhD degree in electrical engineering from Stanford University. Following completion of his education, he worked in industry in Silicon Valley and served as a faculty member in the Department of Electrical Engineering at Stanford. He was Professor of Electrical Engineering at the University of Newcastle, Australia from 1967 until 1981 and is now a Distinguished Professor at the Australian National University and Distinguished Researcher in National ICT Australia Ltd. His interests are in control and signal processing. He is a Fellow of the IEEE, Royal Society London, Australian Academy of Science, Australian Academy of Technological Sciences and Engineering, Honorary Fellow of the Institution of Engineers, Australia, and Foreign Associate of the US National Academy of Engineering. He holds doctorates (honoris causa) from the Université Catholique de Louvain, Belgium, Swiss Federal Institute of Technology, Zürich, Universities of Sydney, Melbourne, New South Wales and Newcastle. He served a term as President of the International Federation of Automatic Control from 1990 to 1993 and as President of the Australian Academy of Science between 1998 and 2002. His awards include the IEEE Control Systems Award of 1997, the 2001 IEEE James H Mulligan, Jr Education Medal, and the Guillemin-Cauer Award, IEEE Circuits and Systems Society in 1992 and 2001, the Bode Prize of the IEEE Control System Society in 1992 and the Senior Prize of the IEEE Transactions on Acoustics, Speech and Signal Processing in 1986.