Refined Composite Multivariate Multiscale Fractional Fuzzy Entropy: Measuring the Dynamical Complexity of Multichannel Financial Data

Refined composite multivariate multiscale fractional fuzzy entropy (RCmvMFFE), which aims to sensitively discriminate different short noisy multichannel financial data, is proposed as a new measure to quantify the complexity dynamics of multichannel time series in this work. To better comprehend the RCmvMFFE measure, the dynamical complexity analyses of multichannel synthetic dataset are comparatively studied with multivariate multiscale fuzzy entropy (mvMFE), refined composite multivariate multiscale fuzzy entropy (RCmvMFE), and refined composite multivariate multiscale fractional fuzzy entropy (RCmvMFFE). Then, these measures are firstly employed to explore actual multichannel financial index series to the best of our knowledge. The empirical analyses report that RCmvMFFE measure is able to deeply and sensitively dig up the market information hidden in the multichannel financial data and can better discriminate markets in different area compared to the traditional measures to some extent.