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Chaos and Deterministic versus Stochastic Non-Linear Modelling

Martin Casdagli
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 54, No. 2 (1992), pp. 303-328
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2346130
Page Count: 26
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Chaos and Deterministic versus Stochastic Non-Linear Modelling
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Abstract

An exploratory technique is introduced for investigating how much of the irregularity in an aperiodic time series is due to low dimensional chaotic dynamics, as opposed to stochastic or high dimensional dynamics. Non-linear models are constructed with a variable smoothing parameter which at one extreme defines a non-linear deterministic model, and at the other extreme defines a linear stochastic model. The accuracy of the resulting short-term forecasts as a function of the smoothing parameter reveals much about the underlying dynamics generating the time series. The technique is applied to a variety of experimental and naturally occuring time series data, and the results are compared with dimension calculations.

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