Robustness of Sample and Multiscale Entropy Estimators in Noisy and Incomplete Time Series

In this work, we analyze and compare two entropy estimators applied to random walk time series. We compare the robustness of multi-scale entropy and sample entropy for different regimes of signal-to-noise ratio. We also compare multi-scale entropy and sample entropy in the case of missing data when simple linear interpolation is adopted to fill the missing data points. In the case of the signal-to-noise comparison, we show by numerical simulations and present strong mathematical arguments that multi-scale entropy is a more resistant estimator to analyze time series. We also show that multi-scale entropy provides a more resistant and accurate estimate of entropy on random walk time series in the scenario of missing data, especially when completing missing data with linear interpolation.