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

  • $\begingroup$ You say CCF, but the image says ACF, which is it? $\endgroup$ Jul 12, 2019 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, 2019 at 13:12
  • $\begingroup$ If you are satisfied by my answer then accept it to close the question . $\endgroup$
    – IrishStat
    Jul 20, 2019 at 13:08

1 Answer 1


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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.