How to calculate the residual of last 3 months using the regression coefficient of this month

[Yao Jin]

Hello everyone!

I have a problem with calculating the residual, the calculation following the steps below:
In each month t，I should:
1. firstly, use daily data from month t-2 through month t to run a FamaFrench 3 factor regression, with formula: excessreturn = b_cons + b_hml*hml + b_smb*smb + b_rmrf*rmrf,
2. define the residual of month t-2 to month t using the regression coefficients that are estimated in step 1,
3. calculate the sd and skewness of month t using the residual defined in step 2, only one sd and one skewness should be computedf or each month,
4. following the same steps for next month t+1.
For example, in jan1989, I run a FF regression using daily data for days from the first day of nov1988 through the end of jan1989, the regression coefficient are estimated, and the daily residuals are calculated using the regression coefficient, the sd and the skewness of jan 1989 are computed using the daily residual from nov1988 to jan1989. In feb1989, I run a FF regression using daily data for days from the first day of dec1988 through the end of feb1989, the regression coefficient are estimated, the residuals of dec1988 to feb1989, the sd and skewness of feb1989 are computed as above.
Many thanks for your help and time, I will be very grateful if you can give some tips!

My panel data contains 7 variables and sorted by date id: date(01.Oct.1988 to 30.Jun.2016) ym(monthly date) id(from 1 to 5883) rmrf smb hml excessreturn.

* Example generated by -dataex-. To install: ssc install dataex
clear
input double(date ym id excessreturn rmrf smb hml)
10503 345 1   -.01936289646965491 -.01127306  .00525148   .0006878
10504 345 1   .004428615495805104  .00170627 -.00085576 -.00139754
10505 345 1             -.0004251  .00996818 -.00446347  .00140606
10506 345 1             -.0004254   .0059196 -.00249881  .00250139
10507 345 1             -.0004254  .00319251  .00030991 -.00277563
10510 345 1             -.0004223 -.00024731  .00422974 -.00149079
10511 345 1             -.0004216 -.00274863  .00377518  .00549557
10512 345 1             -.0004223 -.01161097  .00538493  .00050242
10513 345 1             -.0004223  .00748774 -.00172834  .00512555
10514 345 1             -.0004223  .00450467 -.00003376  .00478568
10517 345 1   .023616446896690534  .01022073 -.00470417  .00443819
10518 345 1   .013620751277013725  -.0011541  .00067627 -.00090353
10519 345 1   .013474597771965517  .00363072  .00327984 -.00298672
10520 345 1             -.0004251  .00043836 -.00042181  .00095446
10521 345 1   .004160660287584015 -.00152961   .0025553   .0011501
10524 345 1   .004094270973417762 -.00565686  .00289626 -.00235665
10525 345 1   -.00491995430789627 -.00111718 -.00253788  .00240047
10526 345 1             -.0004223  .00032483  -.0014962  .00228125
10527 345 1   .017744790651005753  .00044753  .00076314  .00001995
10528 345 1   .008496248264910458  .00309713  .00082262  .00215505
10531 345 1             -.0004216 -.00123408  .00574452  .00172679
10532 346 1             -.0004251  .00287933 -.00061362     .00232
10533 346 1             -.0004233 -.00697585  .00488589  .00050676
10534 346 1             -.0004244 -.00285437  .00281202   .0029033
10535 346 1   .004018632959910915 -.00192175   .0009521  .00358065
10538 346 1             -.0004254 -.00776155   .0027741  .00311697
10539 346 1             -.0004264  .00952688 -.00659687  .00322087
10540 346 1             -.0004254 -.00755174  .00424434  .00203433
10541 346 1             -.0004244   .0000658 -.00040594  .00213749
10542 346 1             -.0004227 -.01219847  .00586826  .00206838
10545 346 1  -.013649725532307035 -.00454815 -.00256307  .00250378
10546 346 1             -.0004233  .00395039  .00248942  .00142837
10547 346 1             -.0004213  .00237563 -.00113014  .00247123
10548 346 1             -.0004223  .00695646 -.00743721 -.00091841
10549 346 1             -.0004244 -.00040684  .00169483  .00343632
10552 346 1   .004060976614823962 -.00631036  .00254483 -.00003972
10553 346 1  -.004886662993443917  .00421284 -.00169779  .00349698
10554 346 1              -.000424  .00715559 -.00209694  .00426515
10555 346 1  -.004908076614824184 -.00287966   .0015931  .00042118
10556 346 1  -.013841080905465748 -.02226113  .00126729 -.00038323
10559 346 1             -.0004548 -.00686149  .00134545  .00068337
10560 346 1 -.0050233243520851146  .00304422 -.00087426 -.00150591
10561 346 1             -.0004606  .00311911  .00006603  .00334213
10562 347 1  -.005045560287584237 -.00880611 -.00284232  .00227736
10563 347 1  -.005018397581225804 -.00939757 -.00306623 -.00021765
10566 347 1             -.0004585 -.00323499 -.00183136  .00373087
10567 347 1   -.00966786949185222  .00212448 -.00235887  .00124775
10568 347 1  -.005130805532577441  .00061133 -.00497766  -.0044441
10569 347 1  -.005102141236861527 -.00950524 -.00064092  .00103131
10570 347 1  -.005172627701375276 -.00722724 -.00339905  .00152378
10573 347 1  -.005192565455980971  .00015278 -.00530367 -.00236584
10574 347 1             -.0004548  .00223309  .00088146  .00437897
10575 347 1  -.005164832368107975 -.00032592 -.00276482  .00010165
10576 347 1             -.0004575  .00387507 -.00047641 -.00151807
10577 347 1    .00905806926717472  .00552013 -.00129807  .00101304
10580 347 1  -.005191265455980971 -.00128961 -7.196e-06  .00584483
10581 347 1             -.0004544  .00347369  -.0033825 -.00407795
10582 347 1             -.0004565 -.00266647 -.00067593 -.00204654
10583 347 1             -.0004551 -.00176227   .0036615 -.00504651
10584 347 1             -.0004517  .00185695 -.00313413  .00019805
10589 347 1             -.0004521  .00926918 -.00593432 -.00186907
10590 347 1             -.0004534  .00813243 -.00295587 -.00200299
10591 347 1             -.0004575 -.00457141  .00446324  .00128521
10595 348 1             -.0004603 -.00625428  .00348006  .00297693
10596 348 1  -.009930748234827456  .00525955  -.0027392 -.00272645
10597 348 1             -.0004603  .00329548 -.00122743 -.00069683
10598 348 1   .009101095144415997  .00577624 -.00208543 -.00008884
10601 348 1             -.0004593   .0099526 -.00551761 -.00026279
10602 348 1   .009059031733438961  .00179973  .00354946  .00461995
10603 348 1             -.0004603 -.00075754  .00440392  .00339012
10604 348 1             -.0004593  .00819852 -.00007103  .00246756
10605 348 1             -.0004593   .0060607   .0023039 -.00229719
10608 348 1   .004205411787819446  .00513847 -.00015631  .00334099
10609 348 1             -.0004613 -.00229445  .00057371 -.00277521
10610 348 1             -.0004613  .01093528 -.00588377 -.00158704
10611 348 1   .027600298631141437  .00921167 -.00284583 -.00459487
10612 348 1             -.0004613  .00313551 -.00084835 -.00063124
10615 348 1   .013138266298920526  .00374158  .00260237 -.00339525
10616 348 1             -.0004623  .00752605 -.00519193  .00170633
10617 348 1             -.0004617 -.00090837  .00317521  .00025433
10618 348 1             -.0004613  .00960258 -.00631583   .0045522
10619 348 1   .008546441027445393  .02269427 -.00559572 -.00016106
10622 348 1    .07504929897242767  .01651668 -.00309322 -.00189771
10623 348 1             -.0004613  .00320827  -.0016308  .00090841
10624 349 1             -.0004603  -.0049795  .00361908 -.00676923
10625 349 1  -.004567342497081826  .00225093  .00262478  .00050828
10626 349 1             -.0004599  .01362544  -.0009618  .00026414
10629 349 1             -.0004603 -.01070708  .00748479 -.00392056
10630 349 1             -.0004613  .01264815 -.00663474 -.00156815
10631 349 1   .003662679857614035   .0107934 -.00043577  .00168113
10632 349 1             -.0004613 -.00688215  .00523801  .00368968
10633 349 1  -.004567342497081826 -.01046152  .00620448  .00326649
10636 349 1  -.004626690171904928 -.01071695  .00314722 -.00381311
10637 349 1             -.0004593  .00668561 -.00352879  .00087794
10638 349 1             -.0004596 -.00106768  .00325114   .0002309
10639 349 1  .0037255299912816687  -.0052176  .00625345 -.00239602
10640 349 1  -.008750670029519073  .00303642 -.00170061 -.00133237
10643 349 1             -.0004579  .00946149 -.00533087  .00049292
10644 349 1             -.0004572 -.00169463  .00397498  .00187004
10645 349 1  -.004658732435981501 -.01182387  .00857389  .00020951
end
format %td date
format %tm ym

[Clyde Schechter]

I don't know what a Fama-Macbeth regression is, so the code below just does an ordinary regression of excessreturn on hml smb and rmrf: change the code accordingly. I assume that after whatever program does Fama-Macbeth regression, the -predict- command is available just as it is after -regress- and can calculate the residual. If not, you will have to modify the code accordingly.

capture program drop one_regression
program define one_regression
    regress excessreturn hml smb rmrf
    predict resid, resid
    summ resid, detail
    gen sd = r(sd)
    gen skewness = r(sd)
    exit
end

by id ym (date),sort: gen lb = ym -2 if _n == 1
by id ym (date): replace lb = ym + 1 if _n > 1
by id ym (date): gen ub = ym

rangerun one_regression, by(id) interval(ym lb ub)
keep if !missing(sd)
keep id ym sd skewness

Notes: You don't say as much, but I assume that you want to do this separately for each id. If that is not the case, remove the -by(id)- option from the -rangerun- command. I also assume that you want only a single observation for each id-ym pair, as the results would just be the same in any other such observation.

-rangerun- is by Robert Picard and is available from SSC. In order to use it, you also need -rangestat-, by Robert Picard, Nick Cox, and Roberto Ferrer, also available from SSC.

[Nick Cox]

 
 gen skewness = r(sd)

is a typo for

 
 gen skewness = r(skewness)

[Yao Jin]

Hello Clyde, thank you very much for your reply and for writing the codes for me! It is exactly what I'm looking for to my issue, thank you for your help!

[Yao Jin]

Hello Nick, thank you very mcuh for catching that typo.

[Robert Picard]

See this recent post for a more efficient tweak on Clyde's code based on the fact that you only need to make these calculations once per month.

[Yao Jin]

Hello Robert, thanks for remind me.