00465 å49c5c30400191ac3c473df77e347c0

470

Russell

•    detecting major departures from the underlying time senes model approximations to dynamical processes

•    detecting cycling among morÄ™ than one or two models

•    identification of the order of models and short fragments in Iow noise environments

•    detecting mis-coded data as distinguished from data points with large noise components

There are a number of potential additional uses including; the use of the phase map movie to assist in interpolating missing observations and the use of the univariate phase map movie in process control. The use of the univariate phase map movie (or a multivariate analogue) in process control has uniÄ…ue potential. This is because the univariate phase map can signal a change in an autocorrelated process, potentially within just a few observations, even while the process is still running in it's usual rangÄ™. In such a setting intervention may be possible long before a signal would be developed in any other control system built upon a static control model.

It is worthy to notÄ™ though that, although this techniÄ…ue has proven valuable as an exploratory tool, it is best at this point in the development of the univariate phase map movie to use traditional methods for fitting models to the data. At some point in the futurÄ™, it may be possible to fit a model directly and efficiently using the univariate phase map itself.

References

Box, G. E. P., Hunter, W. G., Hunter, J. S. (1978), Statistics for Experimenters, John Wiley and Sons, New York, New York.

Box, G. E. P., and Jenkins, G. M. (1976), Time Series Analysis: Forecasting and Control, Holden Day, San Francisco, Califomia.

Falconer, K. J. (1990), Fractal Geometry, Mathematical Foundations and Applications, John Wiley and Sons, New York, New York,

Glass, L., Goldberger, A. L., Courtmancher, M., and Shrier, A. (1987), "Nonlinear Dynamics, Chaos and Complex Cardiac Arrhythmias," Dynamical Chaos, Proceedings of the Royal Society of London, Princeton University Press, New Jersey.

Peterson, I. (1987), "Zeroing in on Chaos," Science News, Yolume 131.