For me this is a very fascinating problem, which I however lack the ability to deal with as well as the nomenclature to describe properly. (Please feel free to edit the title).

The conditions are the following:
I have three volumes of air in which I measure the concentration of a chemical compound. So I have three sets of data: A, B and C, which describe the variation of the compound over time. The measurements are made synchronous with equal and constant time steps.

A is the outdoor air and is not influenced by neither B nor C.

B has its own unique variation due to some internal processes, but can to some extent be influenced by A.

C can be influenced by both A and B.

The big question is:
How can I determine which of A and B influence C and to what extent. A complicating factor is that there is a phase shift, which may vary. It can even be the case that A and B effect C alternately or simultaneously.

I have picked up that some form of Fourier function may come in handy.
What functions and approach would be productive?

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closed as off-topic by MarcoB, Feyre, Kuba Feb 23 '17 at 16:22

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  • 1
    $\begingroup$ I believe you would get excellent answers on the statistical design on CrossValidated.SE $\endgroup$ – corey979 Sep 9 '16 at 18:57
  • $\begingroup$ @corey979 Thanks I will check it out. Never heard of that SE group. $\endgroup$ – MathLind Sep 9 '16 at 19:14
  • $\begingroup$ Before all, I think you must have a look to a time series book. $\endgroup$ – cyrille.piatecki Sep 9 '16 at 19:59
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    $\begingroup$ One measure for this kind of thing is "coherence" en.wikipedia.org/wiki/Coherence_(physics) $\endgroup$ – bill s Sep 9 '16 at 21:25
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    $\begingroup$ Look for "Transfer Function Models" in books like "Time Series Analysis : Univariate and Multivariate Methods" by W. Wei. $\endgroup$ – Anton Antonov Sep 10 '16 at 1:33

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