Assessing the robustness of permutation Jensen–Shannon divergence estimated values for time-series analysis

The permutation Jensen–Shannon divergence has been shown to be a versatile tool of great value for diverse applications within the time-series analysis field. Here, we discuss the robustness of this ordinal measure by analyzing the finite-size bias of its estimated values. Synthetic data generated from several stochastic and chaotic systems were carefully analyzed as testbeds, and relevant conclusions were extracted. Finally, to demonstrate the implementation and utility of these findings in a practical context, we analyze the data generated from a complex real-world system of high interest today: Bitcoin prices.