Abstract
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.
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