From nonlinearity to causality: statistical testing and inference of physical mechanisms underlying complex dynamics

Abstract

Principles and applications of statistical testing as a tool for inference of underlying mechanisms from experimental time series are discussed. The computational realizations of the test null hypothesis known as the surrogate data are introduced within the context of discerning nonlinear dynamics from noise, and discussed in examples of testing for nonlinearity in atmospheric dynamics, solar cycle and brain signals. The concept is further generalized for detection of directional interactions, or causality in bivariate time series.

Acknowledgements

The author would like to thank Aneta Stefanovska for the encouragement to write this article. A. Stefanovska, B. Musizza and the BRACCIA team (http://www.lancs.ac.uk/depts/physics/braccia/) are acknowledged for the cardiorespiratory data and the related cooperation. The author would also like to acknowledge the cooperation with D. Novotná, M. Vejmelka and K. Schindler-Hlaváčková.

This article reviewed a selection of results from several projects supported from different sources. In particular, the EC FP6 project BRACCIA (Contract No 517133 NEST), the Grant Agency of the Academy of Sciences of the Czech Republic projects no. IAA3042401 and IAA300420805, and Institutional Research Plans MSM002160849 and AV0Z10300504 are acknowledged.

Notes

†Obviously, for a linear function F, the model (13) is a special case of(10).