Generalized permutation entropy analysis based on the two-index entropic form Sq,δ.

Permutation entropy (PE) is a novel measure to quantify the complexity of nonlinear time series. In this paper, we propose a generalized permutation entropy ( PEq,δ) based on the recently postulated entropic form, Sq,δ, which was proposed as an unification of the well-known Sq of nonextensive-statistical mechanics and Sδ, a possibly appropriate candidate for the black-hole entropy. We find that PEq,δ with appropriate parameters can amplify minor changes and trends of complexities in comparison to PE. Experiments with this generalized permutation entropy method are performed with both synthetic and stock data showing its power. Results show that PEq,δ is an exponential function of q and the power ( k(δ)) is a constant if δ is determined. Some discussions about k(δ) are provided. Besides, we also find some interesting results about power law.