Multiscale Fractional Cumulative Residual Entropy of Higher-Order Moments for Estimating Uncertainty

Abstract

The fractional cumulative residual entropy is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. In this paper, we present an approach to measure the uncertainty of non-stationary time series named higher-order multiscale fractional cumulative residual entropy. We describe how fractional cumulative residual entropy may be calculated based on second-order, third-order, fourth-order statistical moments and multiscale method. The implementation of higher-order multiscale fractional cumulative residual entropy is illustrated with simulated time series generated by uniform distribution on [0, 1]. Finally, we present the application of higher-order multiscale fractional cumulative residual entropy in logistic map time series and stock markets time series, respectively.