Creating a recursion variable

[Justin Niakamal]

I'm trying to replicate a recursion variable from a paper defined below, but I'm having trouble coding this in or finding a similar problem on the forum. Does anyone have any suggestions as to how to code this in? I've attached a data example below.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float month double change
612   -.004991235657247017
613  -.0003907886751084444
614  -.0004018013641178264
615   .0006069723741721766
616  -.0003405231947763987
617   -.001898208352126396
618   -.001708250381726062
619   .0004951327973063968
620    .002372724815685512
621 -.00011237099952499108
622  -.0010946224222694312
623  -.0006509051015615164
624   -.005122270065494039
625  .00010651547331330669
626   .0006074811462390972
627  -.0013014861316329451
628  -.0005188926319612541
629   .0011688844353914263
630  -.0006228099471545789
631   -.002615094605050272
632 -.00023978680609615388
633   .0023468439977769595
634 -.00036768914480966863
635  -.0007074356476133303
636   .0008620682199795837
637   -.002757046018206255
638   -.004036367199411028
639 -.00044835241560581274
640   .0011642244666922874
641   .0004556775964634774
642  -.0008655306685194653
643  -.0016792169423880399
644  -.0005630953635848979
645   -.005024531278962963
646   -.002627684570536637
647   .0009963658350320426
648 -.00047558246508794255
649  .00014092416617716985
650   .0017915981279021942
651  -.0011096773696968043
652   -.002506033359870319
653   .0006084745578889272
654   .0002629105922167252
655   .0006919548228461192
656  -.0009762794404883923
657 -.00003355802822158083
658   .0007571715633221121
659  -.0012391719361075637
660   .0004830074215247393
661  -.0011976253726078134
662  -.0025890779828434685
663   .0005939042965081853
664   .0030388435814403536
665    -.00104345644145587
666   -.003545362352717296
667   -.000468028487129013
668  -.0022629054253231473
669  -.0010997530228253893
670   .0019434921180616627
671    .002519050389598876
end
format %tmMon-YY month

I apologize for the screenshot. The formula can be found on the bottom of page one here.

[William Lisowski]

Perhaps this yields what you want. I assume that "change" in your data corresponds to the ∆ (delta) between two successive values in your equation (3). If not, it would be particularly helpful if you calculated by hand your desired results for the final few observations and included them in your post.

. generate cd = sum(change)

. replace cd = cd - cd[_N]
(60 real changes made)

. list in 56/l

     +---------------------------------+
     |  month       change          cd |
     |---------------------------------|
 56. | Aug-15   -.00046803   -.0010999 |
 57. | Sep-15   -.00226291   -.0033628 |
 58. | Oct-15   -.00109975   -.0044625 |
 59. | Nov-15    .00194349   -.0025191 |
 60. | Dec-15    .00251905           0 |
     +---------------------------------+

[Justin Niakamal]

Thanks, William Lisowski, I'll try and work this into what I've put together (sorry for the late reply, I was moving over the weekend ).