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I need metrics to quantify and compare the extent of periodicity between any two given time series, considering the time series were "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.

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    $\begingroup$ I guess you want to do some fourier analysis... $\endgroup$
    – Per Alexandersson
    Sep 2, 2015 at 13:35
  • $\begingroup$ I could perform Fourier transform and find the highest amplitude frequency (lower one is there are many), but can I use this amplitude value directly to compare any two time series to compare the extent to which they are periodic? Is there any normalization that needs to be done? I also want to know if there is a way to quantify periodicity using fractal analysis. $\endgroup$
    – np20
    Sep 2, 2015 at 13:59
  • $\begingroup$ Is there a specific reason that you want to use fractal? $\endgroup$
    – Creator
    Sep 19, 2015 at 21:06

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