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How should one proceed when doing a transfer function model of a dependent Y and independent X, when an intervention affects both Y and X?

I learned the order should be :

  1. Prewhiten X, Filter Y, determine transfer model with CCF
  2. Conduct intervention analysis on Y
  3. Run Arimax with X and interventions, p,d,q = 0,0,0
  4. Analyze residuals to determine p,d,q. Rerun Arimax with x, interventions, and p,d,q.

But, what do we do when the interventions also affect x? Is it still a good idea to use Arima in this case?

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1 Answer 1

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2) Should be

Conduct Intervention on residuals from Step 1

If an intervention affects X and Y it is not an intervention . if an intervention affects Y GIVEN the effect of X it is an intervention.

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  • $\begingroup$ The residuals from step one is the filtered y, so to clarify, you conduct intervention analysis on the filtered Y? That is very useful information! You say that when an intervention affects X and Y, it is not an intervention. If a change in a law affects X and Y, would the effect be seen by the regression, and therefore one would not need to model the intervention? Because, the effect might decay faster in X than in Y, for example. $\endgroup$
    – Frank
    Commented Jul 11, 2019 at 0:06
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    $\begingroup$ interventions have nothing whatsoever to do with decay ...they are the point estimates of the change in the expected value for a particular point in time. If an intervention variable of the form 3/[1-.5B]) for example was detected this would mean a bump of 3 for the first period , a bump of 1.5 for the second period out etc . .75 for the third ... $\endgroup$
    – IrishStat
    Commented Jul 11, 2019 at 0:12
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    $\begingroup$ to answer your first comment ..... the pre-whitening filters are only used to IDENTIFY the form of the transfer between y and x . Once you have the INITIAL form ... you estimate the TF model and the residuals form that model might suggest the need for augmentation. $\endgroup$
    – IrishStat
    Commented Jul 11, 2019 at 0:19
  • $\begingroup$ Does this sound right ? (step1) Prewhiten (step2) model Y ~ Arimax with X, p,q = 0,0 (step3) Conduct an intervention analysis on the residuals (step4) Arimax with X and interventions, p,q = 0,0 (step5) determine p,q with ACF, PACF on residuals (step6) final model Arimax(p,d,q) with X and Interventions $\endgroup$
    – Frank
    Commented Jul 11, 2019 at 0:26
  • $\begingroup$ By a decaying intervention, I mean something like a mean shift that returns to the original mean over time. If this mean shift affects both X and Y, but returns to the mean faster in X than in Y... how would you model this? $\endgroup$
    – Frank
    Commented Jul 11, 2019 at 0:27

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