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I would like to verify the similarity of two time series. So far I have resampled and interpolated one time series, so that the two have synchronous time.

Next I have computed the relative difference to measure the difference between the two series. I have been recommended to compute the auto-correlation error by summing up the relative difference at each time lag. However, I am unsure if this is the correct way to go as I read that auto-correlational is computing the similarity of one series with itself.

Is cross-correlation what I need? Or RMSE? I don't need to measure how one series affect the other, but rather a difference (error).

Another question is that without resampling and interpolation, how I can compute the time lag between two time series? One series has way more samples than the other.

EDIT:

When I plotted the cross-correlation between the two series I get the below image. Does this mean that the two series are almost without error?

Cross-correlation

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If I were you, I would try first to study the cross-correlation between the two original series (with synchronous time) and see what conclusions you get.

In my opinion, that's the simplest way to get information about similarity (or "simultaneous correlation") and influence (or "lagged correlation") between the series (you also get autocorrelations of each series for free, but that's not what we are focusing on!) If that works for you, then I wouldn't go any further into more complicated analysis

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  • $\begingroup$ Thank you for the suggestion. When I computed the cross-correlation, I get that all the lag values are close to 1. Does this mean that my two series are almost without error? $\endgroup$ – solaris Jun 13 at 7:08
  • $\begingroup$ Well, if there is high correlation at lag 0, then the series look alike. If there is also high correlation for other lag values, this means the series look alike and are also very autocorrelated $\endgroup$ – David Jun 13 at 7:13

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