Horizontal visibility graphs discriminate randomness from chaos

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In the last years, some methods mapping time series to network representations have been proposed. The purpose is to investigate on the properties of the series through graph theoretical tools recently developed in the core of the celebrated complex network theory. Among some other methods, the so called visibility algorithm has received much attention, since it has been shown that series correlations are captured by the algorithm and translated in the associated graph, opening the possibility of building fruitful connections between time series analysis, nonlinear dynamics, and graph theory. Here we show that the horizontal visibility algorithm is able to distinguish between correlated stochastic, uncorrelated and chaotic processes just by calculating a single parameter λ in the associated graphs. We show that in every case the series maps into a graph with exponential degree distribution P (k) ∼ exp(−λk), where the value of λ characterizes the process.

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