Multi-scale entropy analysis and Hurst exponent

Abstract

Several methods exist for measuring the complexity in a system through analysis of its associated time series. Multi-scale entropy appears as a successful method on this matter. It has been applied in many disciplines with great achievements. For example by analysis of the bio-signals, we are able to diagnose various diseases. However, in most versions for the multi-scale entropy the examined time series is analyzed qualitatively. In this study, we try to present a quantitative picture for the multi-scale entropy analysis. Particularly, we focus on finding relation between the result of the multi-scale analysis and the Hurst exponent which quantifies the persistence in time series. For this purpose, the fractional Gaussian noise time series with different Hurst exponents are analyzed by the multi-scale entropy method and the results are fitted to a decreasing q-exponential function. We observe remarkable relation between the function parameters and Hurst exponent. This function can simulate the result of analysis for the white noise to the 1∕f noise.