A direct method to detect deterministic and stochastic properties of data

Abstract

A fundamental question of data analysis is how to distinguish noise corrupted deterministic chaotic data from time-correlated stochastic fluctuations. For short data, even the distinction of chaotic signals from uncorrelated stochastic data may be a hard task, since trajectory properties may not be properly reflected by the data. Despite its importance, direct tests of chaos vs. stochasticity in finite time series including the most typical case of largely noise corrupted time series still lack of a definitive quantification. Here we present a novel approach based on recurrence analysis, a nonlinear level approach to deal with data. Namely, we use the probability of occurrence of recurrence microstates or ordinal permutation patterns, to overcome limitations in the quantification of deterministic and stochastic data. The main idea of the approach is the identification of how recurrence microstates and permutation patterns are affected by time reversibility of data, and how its behavior can be used to distinguish stochastic and deterministic data. We demonstrate its efficiency for a bunch of paradigmatic systems under strong noise influence, as well as for real-world data, covering electronic circuit, sound vocalization and human speeches, neuronal activity, heart beat data, and geomagnetic indexes. Interestingly, we identify this way squid neuronal activity as from deterministic, human speech data as from non-stationary deterministic, but heart rate data from stochastic origin. Our results support the conclusion that the method distinguishes deterministic from stochastic fluctuations in simulated and empirical data even under strong noise corruption, finding applications involving various areas of science and technology. In particular, for deterministic signals, the quantification of chaotic behavior may be of fundamental importance because it is believed that chaotic properties of some systems play important functional roles, opening doors to a better understanding and/or control of the physical mechanisms behind the generation of the signals.

How to Compute Suitable Vicinity Parameter and Sampling Time of Recurrence Analysis

“…Each record lasts several seconds and is sampled at 125 kHz [10,22]. The data is open and free available at https://https://physionet.org/content/sgamp/1.0.0/ and recently characterized as deterministic [23]. To use a similar procedure used for the deterministic and stochastic signals analyzed so far, we have segmented the data into 1, 000 data-points and an appropriated vicinity parameters have been computed for each segment, computing S(τ) ≡ MAX ε S(ε, τ).…”