Generalized information entropy analysis of financial time series

Generalized information entropy has been widely applied to analyzing complex systems. In this paper, we propose the weighted multiscale Rényi permutation entropy (MSWRPE) based on the weight assigned to each vector as a novel technique to consider the amplitude information. Rényi permutation entropy (RPE) has a parameter q for non-extensivity compared to Shannon permutation entropy (PE). Hence we speculate that RPE has a better sensitivity to patterns extracted from signals containing amplitude information and a better robustness to noise compared to PE. Firstly, we perform the multiscale Rényi permutation entropy (MSRPE) and MSWRPE methods on synthetic data. We find that MSWRPE suits better signals containing considerable amplitude information and is successful to consider the multiple time scales inherent in the financial systems. The finding is also verified in four different stock markets. Then, we make a comparison between MSWRPE and weighted multiscale permutation entropy (MSWPE) on different stock markets. The conclusion is that the MSWRPE method has a better characterization than MSWPE. For q<1, different markets have the same law on MSWRPE, while HSI can be distinguished from the other markets for q>1, which is more obvious when m=7.