On the characterization of the deterministic/stochastic and linear/nonlinear nature of time series

On the characterization of the deterministic/stochastic and linear/nonlinear nature of time series

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Article ID: iaor20091468
Country: United Kingdom
Volume: 464
Issue: 2093
Start Page Number: 1141
End Page Number: 1160
Publication Date: May 2008
Journal: Proc Royal Soc A: Mathematical, Physical & Engineering Sciences
Authors: , , , ,
Keywords: artificial intelligence
Abstract:

The need for the characterization of real-world signals in terms of their linear, nonlinear, deterministic and stochastic nature is highlighted and a novel framework for signal modality characterization is presented. A comprehensive analysis of signal nonlinearity characterization methods is provided, and based upon local predictability in phase space, a new criterion for qualitative performance assessment in machine learning is introduced. This is achieved based on a simultaneous assessment of nonlinearity and uncertainty within a real-world signal. Next for a given embedding dimension, based on the target variance of delay vectors, a novel framework for heterogeneous data fusion is introduced. The proposed signal modality characterization framework is verified by comprehensive simulations and comparison against other established methods. Case studies covering a range of machine learning applications support the analysis.

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