Yet you are given their time index values, meaning you have more than the unordered simultaneous pairs you presented in the example.
The example data (here they are again) is a time series, not a set of unordered pairs. (Time is proportional to line number.)
No means whatsoever?
None whatsoever (assuming the random noise that drives the process is truly random, or at least unknowable—guessing the pseudo-RNG algorithm and its seed doesn’t count).
Consider this challenge open to anyone who thinks that there is mutual information between the two columns: calculate it. Prove the validity of the computation by calculating information about the second column given only the first, for a new file generated by the same method.
The example data (here they are again) is a time series, not a set of unordered pairs. (Time is proportional to line number.)
None whatsoever (assuming the random noise that drives the process is truly random, or at least unknowable—guessing the pseudo-RNG algorithm and its seed doesn’t count).
Consider this challenge open to anyone who thinks that there is mutual information between the two columns: calculate it. Prove the validity of the computation by calculating information about the second column given only the first, for a new file generated by the same method.