Prediction and geometry of chaotic time series

dc.contributor.advisorFrenzen, Christopher
dc.contributor.advisorBeaver, Philip
dc.contributor.authorLeonardi, Mary L
dc.contributor.departmentMathematics
dc.date.accessioned2012-08-09T19:23:03Z
dc.date.available2012-08-09T19:23:03Z
dc.date.issued1997-06
dc.description.abstractThis 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 beneficialen_US
dc.description.distributionstatementApproved for public release; distribution is unlimited.
dc.description.serviceCaptain, United States Marine Corpsen_US
dc.description.urihttp://archive.org/details/predictionndgeom109458843
dc.identifier.urihttps://hdl.handle.net/10945/8843
dc.language.isoeng
dc.publisherMonterey, California. Naval Postgraduate Schoolen_US
dc.subject.authorAttractor Reconstructionen_US
dc.subject.authorChaosen_US
dc.subject.authorPredictionen_US
dc.subject.authorState Space Reconstructionen_US
dc.subject.authorTime Seriesen_US
dc.subject.lcshCHAOSen_US
dc.titlePrediction and geometry of chaotic time seriesen_US
dspace.entity.typePublication
etd.thesisdegree.disciplineApplied Mathematicsen_US
etd.thesisdegree.grantorNaval Postgraduate Schoolen_US
etd.thesisdegree.levelMastersen_US
etd.thesisdegree.nameM.S. in Applied Mathematicsen_US
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