Refined two-index entropy and multiscale analysis for complex system

摘要

As a fundamental concept in describing complex system, entropy measure has been proposed to various forms, like Boltzmann-Gibbs (BG) entropy, one-index entropy, two-index entropy, sample entropy, permutation entropy etc. This paper proposes a new two-index entropy S-q,S-delta and we find the new two-index entropy is applicable to measure the complexity of wide range of systems in the terms of randomness and fluctuation range. For more complex system, the value of two-index entropy is smaller and the correlation between parameter delta and entropy S-q,S-delta is weaker. By combining the refined two-index entropy S-q,S-delta with scaling exponent h (delta), this paper analyzes the complexities of simulation series and classifies several financial markets in various regions of the world effectively. (C) 2016 Elsevier B.V. All rights reserved.