Permutation extropy: A new time series complexity measure

Several complexity measures have been proposed to understand the complexity of physiological, financial, biological, and other time series that involve real-world problems. Permutation entropy (PE), fractal dimension and Lyapunov exponents are such complexity parameters out of many. The enormous use of PE in specifying complexity of chaotic time series motivates us to propose an alternative complexity parameter in this paper, known as the permutation extropy (PExt) measure. Here, we combine the ideas behind the PE and extropy to construct this new measure. We then validate the proposed measure using logistic, Hénon and Burger chaotic maps. Further, we apply the proposed complexity measure to study the impact of Covid-19 on financial stock market time series data set and to analyze the situation of Covid in India across different phases, considering the WHO data set. The proposed measure demonstrates robustness, fast calculation and invariant with respect to monotonous nonlinear transformation like PE.