ICA is a relatively new statistical methodology, also known as "blind source
separation", to approach the so called "cocktail-party" problem.
Roughly speaking,
the "cocktail-party" problem could be casted as a special case of the
broad classical and still challenging subject of "inverse problems",
commonly found in
Astronomy and Signal Processing:
given the image find the sources . Essentially,
ICA technique allow us to find separation of the observed signal (image)
as a combination of sources (unknown at the
beginning) with reduced statistical dependence at not only second
order (cross-correlations), but also at higher orders as well (e.g.
fourth-order cross-cumulants).
Besides the classical problems already mentioned, ICA has also found
direct applications in the world of finance. The basic idea is to apply
such methodology to try to uncover hidden patterns
in the observed financial data (i.e. foreign exchange rates
or stock returns)
such as long term memory, mean reverting behaviour,
fractional integration effects, etc.
Currently, I am working on a research project involving further
explorations on the application of ICA in the understanding of the
underlying processes, perhaps laws, governing the
dynamics of financial markets. Details will be provided as the project
progress.
Click on
[cse610_report.pdf]
or
[cse610_report.ps.gz]
to download a copy of the most recent
report in pdf or postscript formats.
References
A readable introduction to ICA is:
Hyvärinen, A., and Oja, E. (2000). "Independent component analysis:
algorithms and applications", Neural Networks, 13 ,
411-430.
Comprehensive surveys or reviews on ICA are:
Hyvärinen, A. (1999) Survey on Independent Component Analysis,
Neural Computing Surveys, 2 , 94-128.
Lee, T. (1998). "Independent Component Analysis. Theory and
Applications", Kluwer Academic Publishers.
Explicit Applications of ICA to finance can be found in:
Moody, J. and Howard, Y. (1999). "Term structure of interactions of
foreign exchange rates", Computational Finance-Proceedings of the
sixth Int'l conference, New York. Edited by Abu-Mostafa et. al.
MIT press.
Moody, J. and Wu, L. (1998). "High frequency foreign exchange rates:
price behaviour analysis and 'true price models'", Nonlinear Modeling
of High Frequency Financial Times Series, pages 23-47, Willey.
Back, A.D and Weigend, A. S. (1997). "A first application of
independent component annalysis to extracting structure from stocks
returns",
International Journal of Neural System, 8 ,
473-484.
