Detecting high-dimensional determinism in time series with application to human movement data

We numerically investigate the ability of a statistic to detect determinism in time series generated by high-dimensional continuous chaotic systems. This recently introduced statistic (denoted VE2VE2) is derived from the averaged false nearest neighbors method for analyzing data. Using surrogate data tests, we show that the proposed statistic is able to discriminate high-dimensional chaotic data from their stochastic counterparts. By analyzing the effect of the length of the available data, we show that the proposed criterion is efficient for relatively short time series. Finally, we apply the method to real-world data from biomechanics, namely postural sway time series. In this case, the results led us to exclude the hypothesis of nonlinear deterministic underlying dynamics for the observed phenomena.