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For time-series data, we can calculate its n-length entropy to evaluate the predictability of two kinds of bounds.
The first kind of entropy S^unc is calculated with only the PDF of time-series data, that is, the entropy is not consideration of time correlation among the data.
On the other hand, if the all correlations among time-series data are explored, it will make high certainty for data. However, such target is too complexity to be realized. Here we use Lempel-Ziv algorithm to dig the relationship among the time-series data in some level and calculate its entropy as S^actual, and S^actual is smaller than S^unc.
With two entropies, using Fano's inequality, the up bound 〖 ¥Ð〗^max and low bound 〖 ¥Ð〗^unc of predictable of time-series data can be calculated for evaluation of probability that time-series can be perfectly predicted.
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IEEE/ICACT20210239 Slide.10
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