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I am studying pre whitening and cross correlation functions. I read somewhere... I forgot where, that there are patterns which tell you which lags of each variable to take.

In this image, lags of X correlate with Y, and then a decay of correlation begins at lag 3 of X. I read that, when modeling Y with Arimax, a pattern like this means I should use lag 3 of X and lag 1 of Y.

My question is... why? I was told to use these lags when I see this pattern, but I was not told why!

. prewhitened ccf

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  • $\begingroup$ You say CCF, but the image says ACF, which is it? $\endgroup$ – user2974951 Jul 12 '19 at 13:07
  • $\begingroup$ It is a CCF between residuals of X fitted with Arima and Y values filtered with the Arima model used on X. $\endgroup$ – Frank Jul 12 '19 at 13:12
  • $\begingroup$ If you are satisfied by my answer then accept it to close the question . $\endgroup$ – IrishStat Jul 20 '19 at 13:08
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You may have gotten it by searching GOOGLE for "REILLY-WEI TIME SERIES" pointing to a readable text book on time series analysis.

The CCF data that you showed is from the classic GASX-GASY example enter image description here suggesting enter image description here using enter image description here to identify starting model.

You might also have seen it here http://viewer.zmags.com/publication/9d4dc62a#/9d4dc62a/66 where AUTOBOX ( a piece of software that I have helped to develop)

In terms of intuition AFTER you have decided that there is a possible 3 period delay .. the ccf generally appear to have a dampening pattern roughly like an ar(1) thus the dynamic structure (denominator) is set to 1.

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