I checked your references and they agree with me: Both clearly state that the second series (and third for wolfram) is derived from the first; the wolfram version has a total of three series but in which the two complex functions f and g are both derived from the same starting series. In both cases there is only one driving variable, everything else is derived. If you start with two series, you want ordinary correlation, not cross-correlation.
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Isn't the point of cross-correlation to determine if two datasets are, or approximate to, being described by the same series, but with different offsets?
Therefore the OPs talk of "two series" is correct until the determination is made that they might actually be the same series.
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
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The point of cross-correlation is to determine if two signals are similar or not and to which degree. If they are different, no matter the offset, the cross-correlation value will be very small (close to 0).
In the case of auto-correlation, the signal is cross-correlated to itself. So, it will be always picked (1.0) at 0 lag.
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Actually, he has to provide the offset on one and then instead of cross-correlating with the original he has to (standard-) correlate that result with the other. I know enough to provide a better answer now...
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Wikipedia states clearly:
"In signal processing, cross-correlation is a measure of similarity of TWO waveforms as a function of a time-lag applied to one of them.".
TWO waveforms or TWO signals, etc... (two not one).
You are confusing cross-correlation with auto-correlation... The auto-correlation is the correlation of a signal with itself.
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