Stephen J. Guastello, Marquette University, Milwaukee, WI

Abstract: The unique demands for analyzing nonlinear time series produced by complex systems have generated a paradigm shift in statistical theory and application in much the same way as nonlinear dynamics have augmented the understanding of specific phenomena in the life and social sciences. Topics covered include: the statistical computation of the fractal dimensions, ergodicity, strategic use of nonlinear model libraries, identifying oscillators, state space analysis and entropy, time delays and the production of emergents, and quantum computing of fractal images. Substantive applications include US unemployment, political affiliation in the Netherlands, bipolar disorder, biomechanics, heart rate complexity, Bitcoin and other market prices, temperature anomalies and climate change, and economic growth.

Keywords: fractal, ergodicity, oscillator, state space analysis, entropy, time delays