Ordinal spectrum: a frequency domain characterization of complex time series

Abstract: Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to characterise the complexity of a time series. In contrasts with other nonlinear mapping functions (e.g. the state-space reconstruction) the proposed representation is a natural approach to distinguish, in a frequency domain, a chaotic behavior. We test the method in different synthetic and real-world data. Our results suggest that the proposed approach may provide new insights into the non-linear oscillations observed in different real data.