A new method for tolerance estimation of multivariate multiscale sample entropy and its application for short-term time series

Multivariate multiscale sample entropy (MMSE) is a robust method to detect the complexity of multivariate system. It is evaluated for a certain value of tolerance parameter r which is mainly calculated from common acknowledged range. This kind of selection of r is not suitable for short-term time series and may lead to the unreliable detection. To reduce the impact of limited range of r, we apply cumulative histogram method to estimate the range of r. It is data-driven and needs no parameters. Moreover, we use secondary statistics, AvgMMSE and SDMMSE rather than the single value of MMSE to detect the complexity of signals and differentiate them. Several time series, either generated from chaotic or stochastic systems, are analyzed to demonstrate the approach. The core achievement of this experiment is the stability and classification for short-term time series. Then we apply this method to financial time series. Empirical results show that the proposed method is vigorous enough to classify different stock indices over different periods.