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Non-stationarity is a general issue with the estimation of Shannon Entropy from a time series. It affects estimation attempts of all measures. This is because the concept of Shannon Entropy is related to the distribution of a random variable, not to any particular realization of the r.v.

What we do in these cases is to make stationary the time series that are not (e.g. by computing the differences between consecutive observations).

I would like to do something different. I have hourly data for many days and many years of observations. Maybe is it possible to "sacrifice" many of them in order to obtain an entropy estimation that is more robust to non-stationarity of the data? For example, since I have hourly data, I could build a daily entropy estimator by averaging the hourly entropy values. (But I do not know if this operation make the estimator more robust to non-stationarity).

What would you do

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    $\begingroup$ How do you define Shannon entropy for a nonstationary time series? There is no fixed underlying distribution to extract probabilities from. $\endgroup$ Jun 21, 2020 at 12:29

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