The identification of critical fluctuations and phase transitions in short term and coarse-grained time series—a method for the real-time monitoring of human change processes

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Abstract
We introduce two complementary measures for the identification of critical instabilities and fluctuations in natural time series: the degree of fluctuations F and the distribution parameter D. Both are valid measures even of short and coarse-grained data sets, as demonstrated by artificial data from the logistic map (Feigenbaum-Scenario). A comparison is made with the application of the positive Lyapunov exponent to time series and another recently developed complexity measure—the Permutation Entropy. The results justify the application of the measures within computer-based real-time monitoring systems of human change processes. Results from process-outcome research in psychotherapy and functional neuroimaging of psychotherapy processes are provided as examples for the practical and scientific applications of the proposed measures.

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