Prediction and geometry of chaotic time series
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Authors
Leonardi, Mary L
Subjects
Attractor Reconstruction
Chaos
Prediction
State Space Reconstruction
Time Series
Chaos
Prediction
State Space Reconstruction
Time Series
Advisors
Frenzen, Christopher
Beaver, Philip
Date of Issue
1997-06
Date
Publisher
Monterey, California. Naval Postgraduate School
Language
eng
Abstract
This thesis examines the topic of chaotic time series. An overview of chaos, dynamical systems, and traditional approaches to time series analysis is provided, followed by an examination of state space reconstruction. State space reconstruction is a nonlinear, deterministic approach whose goal is to use the immediate past behavior of the time series to reconstruct the current state of the system. The choice of delay parameter and embedding dimension are crucial to this reconstruction. Once the state space has been properly reconstructed, one can address the issue of whether apparently random data has come from a low- dimensional, chaotic (deterministic) source or from a random process. Specific techniques for making this determination include attractor reconstruction, estimation of fractal dimension and Lyapunov exponents, and short-term prediction. If the time series data appears to be from a low-dimensional chaotic source, then one can predict the continuation of the data in the short term. This is the inverse problem of dynamical systems. In this thesis, the technique of local fitting is used to accomplish the prediction. Finally, the issue of noisy data is treated, with the purpose of highlighting where further research may be beneficial
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Description
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Department
Mathematics
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Distribution Statement
Approved for public release; distribution is unlimited.