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I am interested in finding a statistic that tracks the unpredictability of a time series. For simplicity sake, assume that each value in the time series is either 1 or 0. So for example, the following two time series are entirely predictable TS1: 1 1 1 1 1 1 1 1 TS2: 0 1 0 1 0 1 0 1 0 1 0 1

However, the following time series is not that predictable: TS3: 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1

I am looking for a statistic that given a time series, would return a number between 0 and 1 with 0 indicating that the series is completely predictable and 1 indicating the series in completely unpredictable.

I looked at some entropy measures like Kolmogorov Complexity and Shannon entropy, but neither seem to fit my requirement. In Kolmogorov complexity, the statistic value changes depending on the length of the time series (as in "1 0 1 0 1" and "1 0 1 0" have different complexities, so its not possible to compare predictability of two time series with differing number of observations). In Shannon entropy, the order of observations didn't seem to matter.

Any pointers on what would be a good statistic for my requirement?

If you are trying to forecast the time series based on its history, use the entropy rate.

– Emre – 2015-01-06T05:10:56.850