Tangle: A New Measure of Time Series Complexity.

Dynamical systems analysis and the study of time series data provide a rich source of information for researchers interested in studying psychological phenomena. While many methods exist for quantifying linear behavior from a given time series, considerably fewer methods exist for quantifying complex and nonlinear time series. Of existing methods for quantifying complex and nonlinear time series, most either: a) require a restrictive number of data points, b) are highly sensitive to noise, c) are technically challenging to implement, or d) require researchers to heuristically set many hyper-parameters. Each of these requirements impedes the utility of measures of temporal complexity in psychological science. We propose a new complexity metric, , that overcomes these restrictions. Tangle is applicable to time series with as few as 50 time points, is robust to noise, and requires only iterative matrix multiplication to be calculated.