A Personal Overview of Non-Linear Time Series Analysis from a Chaos Perspective [with Discussion and Rejoinder]

A personal overview of non-linear time series from a chaos perspective is given in an informal but, it is hoped, informative style. Recent developments which, in a radically new way, formulate the notion of initial-value sensitivity with special reference to stochastic dynamical systems are surveyed...

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Bibliographic Details
Published in:Scandinavian journal of statistics 1995-12, Vol.22 (4), p.399-445
Main Authors: Tong, Howell, Chan, K. S., Cox, D. R., Cutler, Colleen D., D. Guégan, Jensen, Jens Ledet, Johansen, Søren, Lawrance, A. J., Lebaron, Blake, Ozaki, T., Nychka, Douglas W., Ellner, Stephen, Barbara A. Bailey, Gallant, A. R., Smith, L. R., Smith, R. L., Rodney C. L. Wolff
Format: Article
Language:English
Subjects:
Chaos theory
Consistent estimators
Correlations
Determinism
Dynamical systems
Skeleton
Statistics
Time series
Time series analysis
Time series models
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Summary:A personal overview of non-linear time series from a chaos perspective is given in an informal but, it is hoped, informative style. Recent developments which, in a radically new way, formulate the notion of initial-value sensitivity with special reference to stochastic dynamical systems are surveyed. Its practical importance in prediction is highlighted and its statistical estimation included by appealing to the modern technique of locally linear non-parametric regression. The related notions of an embedding dimension and correlation dimension are also surveyed from the statistical stand-point. It is shown that deterministic dynamical systems theory, including chaos, has much to offer to the subject. In return, some current results in the subject are summarized, which suggest that some of the standard practice in the former may have to be revised when dealing with real noisy data. Several open problems are identified.
ISSN:0303-6898
1467-9469