I need metrics to quantify the extent of periodicity between of a time series (for comparison with other time series), considering the time series is almost periodic. By almost periodic I mean: if I were to take one time series and segment (consider it is possible and allowed to do this) its periods, there would be a fairly strong cross-correlation (say >8) between any two of these segmented periods within one time series.
The simplest metric I can think of is average of cross-correlations between pairs of segmented periods within the time series. I would expect the time series with a higher average cross-correlation to be more periodic than a time series with a lower average cross-correlation measure. This seems intuitively fair, because if we were to take the average cross-correlation measure for a perfectly periodic time series say a sinusoid, I would expect the cross-correlation between any two of this periodic segments to be one (as they are the same) and hence find the average cross-correlation among a set of such segmented periods to be 1 (which is the maximum value in this metric).
I would also like to know if there is a way to do it using fractal analyses, considering only one time-scale resolution (self similarity i.e. of the periods in one time scale and not in multiple time scale resolutions)? I understand that the point of use of fractal analysis is that it considers multiple time-scales, but I want to understand its use and where it stands from the perspective of single time-scale resolution. I also want to see if there is a generalization of the the measurement of self similarity when time scales are varied differently (single time scale being an extreme case where it is not varied at all).
I am currently using fractal dimension measures as heuristics to quantify the smoothness/roughness of a time series. If I could find a metric using fractal analysis to also quantify extents of periodicity of time series, it would complement the other time series analyses I am performing.
Here's a link to a csv with two vectors that I would like to compare the extent of periodicity of, for example.