Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series Dynamics

Abstract

Within this chapter, a practical introduction to a nonlinear analysis framework tailored for time-series data is provided, enabling the safe quantification of underlying evolutionary dynamics, which describe the referring empirical data generating process. Furthermore, its application provides the possibility to distinct between underlying chaotic versus stochastic dynamics. In addition, an optional combination with (strange) attractor reconstruction algorithms to visualize the denoted system’s dynamics is possible. Since the framework builds upon a large variety of algorithms and methods, its application is by far trivial, especially, in hindsight of reconstruction algorithms for (strange) attractors. Therefore, a general implementation and application guideline for the correct algorithm specifications and avoidance of pitfalls or other unfavorable settings is proposed and respective (graphical) empirical examples are shown. It is intended to provide the readers the possibility to incorporate the proposed analysis framework themselves and to conduct the analyses and reconstructions properly with correct specifications and to be knowledgeable about misleading propositions or parameter choices. Finally, concluding remarks, future avenues of research and future refinements of the framework are proposed.