Analysis of financial stock markets through the multiscale cross-distribution entropy based on the Tsallis entropy

In this paper, we propose a multiscale cross-distribution entropy (MCDE) method based on the Tsallis entropy to analyze financial stock markets. In order to evaluate the effectiveness of this method, we employ it into ARFIMA models. Then, applying the proposed method to analyze financial time series, we conclude that it provides us more exact, detailed and clearer information about the relationships between pairs of financial stock markets in comparison with the multiscale cross-sample entropy. Furthermore, the results show that the embedding dimension m has little influence on MCDE. The stability of financial time series could be affected by the order q. Moreover, the MCDE results of q>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q > 0$$\end{document} tend to be more stable than the results obtained by q<0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q < 0$$\end{document}, and it may arise from producing amounts of entropy as q<0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q < 0$$\end{document}. The larger the entropy is, the more active the financial time series is.