Analysis of complex time series using refined composite multiscale entropy

• A refined composite multiscale entropy (RCMSE) method is proposed.
• RCMSE can reduce the probability of inducing undefined entropy.
• Compared with MSE, RCMSE is more precise and reliable for short-term time series.

Multiscale entropy (MSE) is an effective algorithm for measuring the complexity of a time series that has been applied in many fields successfully. However, MSE may yield an inaccurate estimation of entropy or induce undefined entropy because the coarse-graining procedure reduces the length of a time series considerably at large scales. Composite multiscale entropy (CMSE) was recently proposed to improve the accuracy of MSE, but it does not resolve undefined entropy. Here we propose a refined composite multiscale entropy (RCMSE) to improve CMSE. For short time series analyses, we demonstrate that RCMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy.