Interpreting SARIMA coefficients

[Jade Khalife]

Hi Statalist,

After running a SARIMA model that necessitated seasonal differencing, I am unable to translate the coefficient for level/step change (here -1.636669) in pre-differenced value terms.
i.e. in a manner that I could write up as % change in visit_rate in post-intervention period, relative to pre-intervention period.
Is there an approach to get this using Stata?

I would very much appreciate any feedback or guidance.

arima visit_rate level, arima(0,0,1) sarima(0,1,1,12)

visit_rate is my dependent variable.
level is a step function, representing an intervention (abrupt, permanent change).

Results:


Example of data:

* Example generated by -dataex-. For more info, type help dataex
clear
input float yearmonth double visit_rate float level
612  5.480198860168457 0
613  4.896322250366211 0
614 1.7097431421279907 0
615  6.252145290374756 0
616  8.064885139465332 0
617  3.579571485519409 0
618 4.7210845947265625 0
619  8.554865837097168 0
620  3.740657091140747 0
621   3.05062198638916 0
622  7.611184597015381 0
623   6.08182692527771 0
624  4.552469253540039 0
625  5.855523109436035 0
626  9.778051376342773 0
627  4.190736770629883 0
628 4.0452961921691895 0
629  6.049510955810547 0
630 6.9225077629089355 0
631  5.969388008117676 0
632  6.711655139923096 0
633  3.455566883087158 0
634  8.993709564208984 0
635 7.1164703369140625 0
636  5.239231109619141 0
637 12.370341300964355 0
638 6.2445549964904785 0
639  6.980866432189941 0
640 3.1489439010620117 0
641  6.801361560821533 0
642  6.860568523406982 0
643  6.342059135437012 0
644 6.6368489265441895 0
645  4.399888515472412 0
646 6.8126020431518555 0
647  6.515420436859131 0
648  6.218238830566406 0
649  6.525661468505859 0
650   6.71255350112915 0
651  7.386298179626465 0
652  8.236398696899414 0
653  5.731778621673584 0
654  5.851230144500732 0
655  6.391056537628174 0
656   9.78707218170166 0
657  5.335531711578369 0
658  5.253623008728027 0
659  7.071256160736084 0
660   8.88888931274414 0
661  6.722689151763916 0
662  7.236841678619385 0
663  5.594405651092529 0
664  7.518796920776367 0
665  6.201550483703613 0
666  4.477612018585205 0
667  6.428571701049805 0
668  8.333333015441895 0
669  9.219858169555664 0
670  7.258064270019531 0
671  6.097775459289551 0
672   4.93748664855957 0
673   9.86867618560791 0
674  7.934776306152344 0
675  12.59492015838623 0
676  4.205305099487305 0
677  6.224079132080078 0
678  5.248274803161621 0
679   6.01081657409668 0
680 2.2186148166656494 0
681  9.630735397338867 0
682  5.381473064422607 0
683  7.327224969863892 0
684  9.272976875305176 0
685  7.116933822631836 0
686  9.187352180480957 0
687  5.838759422302246 0
688  5.537591457366943 0
689   8.54749584197998 0
690  9.985916137695313 0
691  7.205755233764648 0
692 3.8145639896392822 0
693  3.387136220932007 0
694  5.074203014373779 0
695  8.936643362045288 0
696 12.799083709716797 0
697  9.707664489746094 0
698  6.813113212585449 0
699  6.499801158905029 1
700  6.126939296722412 1
701 14.210118293762207 1
702  4.911804676055908 1
703 7.5343756675720215 1
704  4.770449161529541 1
705  6.923856258392334 1
706 1.8975331783294678 1
707  4.878746390342712 1
708  7.859959602355957 1
709  6.875404357910156 1
710  7.249350070953369 1
711  7.858653545379639 1
712  4.149695873260498 1
713  4.078384876251221 1
714   4.43730354309082 1
715  5.287609100341797 1
716  3.485776901245117 1
717 3.8914425373077393 1
718  7.635324954986572 1
end
format %tm yearmonth

I am using Stata v.16.1.
Thanks.