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

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.