Complexity analysis of time series based on generalized fractional order cumulative residual distribution entropy

Based on the theory of cumulative residual entropy and distribution entropy, this paper proposes a new model cumulative residual distribution entropy (CRDE), which is more suitable for the complexity and risk analysis of time series The new model makes full use of the known information, including not only the information of probability, but also the information about the value of random variables. Additionally, the CRDE considers the potential inherent information of vector-to-vector distance in the state space. By combining theoretical analysis with empirical research, this paper verifies that the new model has more advantages in measuring extreme events and small probability events, with higher consistency, stability and practicability. In this paper, the cumulative residual distribution entropy model is extended to the fractional order. The generalized fractional cumulative residual distribution entropy (GCRDE) can better capture the tiny evolution of time series, which is more advantageous for studying the dynamic characteristics of complex systems. The new model makes up for some shortcomings of traditional models and it can play a guiding role in the study of complex systems in the real world. (C) 2019 Elsevier B.V. All rights reserved.