Multiscale Rényi cumulative residual distribution entropy: Reliability analysis of financial time series

Abstract

In the study of the complexity of time series, information measurement is an effective method to quantify the reliability of dynamic systems, such as financial markets, and its practical use is to identify the state of systems. In this paper, we propose a modification of cumulative residual entropy (CRE) based on cumulative distribution of a random variable, called multiscale Rényi cumulative residual distribution entropy (MRCE), to investigate information content found in more general cases. The CRE is a relevant dynamic measure of uncertainty in reliability studies. Rényi entropy and distribution entropy (DistEn) present diverse means to characterize different complexity behaviors of time series. Compared with the previous complex dynamics methods, the MRCE has larger range showing time series patterns in the field of parameterized transformation. Therefore, MRCE combines the multiscale theory and Rényi cumulative residual distribution entropy (RCE). It is applied to classical discrete distributions, synthetic series and real-world data. Results reveal that MRCE allows a high sensitivity to the predetermined parameters. The improved method enables us to further analyse the complexity of different time series at different scales. Simultaneously, financial time series of stock markets in the same region exhibit obvious similarities.