Loop a time-series regression to predict out-of-sample values

[Jannis Schmidt]

Hello there,
I am quite new to Stata and after desperately searching for a solution in this forum I really need your help.

I have daily data for stock returns and would like to use a 10 year in sample period to predict the returns of the coming year (out of sample) and continue this process until the last date of the dataset is predicted. This would be like a rolling regression but with 1 year steps instead of daily steps.

My data goes from 1/1/1964 till 1/1/2019. I would like to run a regression on stock returns in the period of 1/1/1964 until 1/1/1974 and create a new variable pred_ret that contains the predicted returns for the year 1975 on a daily basis. Next, I would like to use the period 1/1/1965 until 1/1/1975 and predict the daily returns of the year 1976 in the same variable pred_ret. So in the end I will have predicted returns until 2019 that are always based on the betas of a regression of the preceding 10 year period.

As far as I read it in this forum, I will have to use the loop function to run the regression over a certain time and predict values for the next year.

My data looks as following:

* Example generated by -dataex-. To install: ssc install dataex
clear
input int Date double SP500 float(DMon DJan DSummer DToM lag1 movavmonth)
1462    .5450369201135273 0 1 0 1    .6150561    .0914737
1463   .09275823894395199 0 1 0 1    .5450369   .12144153
1466   .22490980208971198 1 1 0 1   .09275824   .11148646
1467  .026432346876929937 0 1 0 0    .2249098    .1174561
1468    .4087262541685617 0 1 0 0  .026432347   .11290492
1469    .3677427336290836 0 1 0 0   .40872625   .13604474
1470  -.05245345096242126 0 1 0 0   .36774275   .15240423
1473 -.026232454736759774 1 1 0 0  -.05245345   .16117047
1474   .18351033877782877 0 1 0 0 -.026232455   .15130717
1475   .36601086611797323 0 1 0 0   .18351033    .1529173
1476  -.11749593208245183 0 1 0 0    .3660109   .15504064
1477   .01305597276325544 0 1 0 0  -.11749593   .11964382
1480  -.19610910127535547 1 1 0 0  .013055973    .1679611
1481    .2744548418127024 0 1 0 0   -.1961091   .14879951
1482    .5336764956149331 0 1 0 0   .27445483   .15508227
1483   .07785752008458488 0 1 0 0    .5336765   .21350373
1484   .02594682295907274 0 1 0 0   .07785752    .2065695
1487 -.038911732012244515 1 1 0 0  .025946824    .1854712
1488   .02593851357128715 0 1 0 0  -.03891173   .17425205
1489   -.6114648795792405 0 1 0 0   .02593851    .1671895
1490   .09130634266269673 0 1 0 0   -.6114649    .1304022
1491    .4423111210359154 0 1 0 1   .09130634   .10546174
1494  -.09090319318391851 1 0 0 1    .4423111   .10096062
1495  -.11700228981167478 0 0 0 1   -.0909032   .09182425
1496  -.16923391728775083 0 0 0 1   -.1170023   .08233213
1497   .23425310035367483 0 0 0 0   -.1692339   .06441651
1498   .32444386386294644 0 0 0 0    .2342531   .07386291
1501  -.16857554075926928 1 0 0 0    .3244439   .06127061
1502   .36274037822475447 0 0 0 0  -.16857554   .05032556
1503   .30987500186526334 0 0 0 0    .3627404   .06452623
1504  -.06448256199605328 0 0 0 0     .309875   .07980385
1505  -.05160516243556825 0 0 0 0  -.06448256   .06853144
1508 -.025821608174692114 1 0 0 0  -.05160516   .05972578
1509  .012911637531657846 0 0 0 0  -.02582161    .0556521
1510   .10321507552329169 0 0 0 0  .012911637   .05370935
1511   .09022362833254678 0 0 0 0   .10321508   .06731499
1515   .07726593924774057 1 0 0 0   .09022363  .034695674
1516                    0 0 0 0 0   .07726594  .036824185
1517   .24429841315724674 0 0 0 0           0  .035070654
1518   -.3215643524049991 0 0 0 0    .2442984   .04855685
1519   .23163051541643703 0 0 0 1  -.32156435  .032009095
1522    .2182680402197652 1 0 0 1    .2316305   .05166679
1523   .32012319648679916 0 0 0 1   .21826804   .05999685
1524  -.19195219796224763 0 0 0 1    .3201232   .07238382
1525 -.012812400104797079 0 0 0 0   -.1919522   .06757196
1526    .3197547092171883 0 0 0 0   -.0128124  .072533384
1529   .02554136888245668 1 0 0 0    .3197547   .07649962
1530   .33137170688734285 0 0 0 0   .02554137   .07395171
1531   .45702887218955274 0 0 0 0    .3313717    .0862098
1532   .16453208903435704 0 0 0 0    .4570289   .11600049
1533   .07583997281823922 0 0 0 0    .1645321     .106562
1536                    0 1 0 0 0   .07583997    .1115713
1537   .22718803301523074 0 0 0 0           0   .10599273
1538   .07561059104284362 0 0 0 0   .22718804   .11176393
1539  -.10082430902006141 0 0 0 0    .0756106   .11659404
1540  -.48035106595272997 0 0 0 0  -.10082431   .11117804
1543  .012672790801534462 1 0 0 0   -.4803511   .08304746
1544  -.17752857707483716 0 0 0 0   .01267279   .07969628
1545    .2408595893239726 0 0 0 0  -.17752858   .06800424
1546     .265535963523251 0 0 0 0    .2408596   .07544032
1550  -.06316301565919895 1 0 0 0   .26553595   .09320308
1551  -.20237294786404786 0 0 0 1  -.06316301   .08538477
1552   .32865027477694564 0 0 0 1  -.20237295   .07168202
1553    .5788351564442354 0 0 0 1    .3286503   .07693832
1554   .30068301469268804 0 0 0 1    .5788351   .08925793
1557   .10001876365197467 1 0 0 0     .300683   .10842682
1558  -.35052490667672453 0 0 0 0   .10001876    .1080064
1559  .012542479326031373 0 0 0 0   -.3505249    .0861716
1560  -.06271935099396053 0 0 0 0   .01254248    .0855526
1561    .1880301459043782 0 0 0 0  -.06271935  .066786356
1564  -.10023932991440215 1 0 0 0   .18803014   .04700751
1565    .2754145542690814 0 0 0 0  -.10023933   .03964517
1566   .12493505341715215 0 0 0 0   .27541456   .05087228
1567    .1372525074207858 0 0 0 0   .12493505   .05682157
1568   .43546694009461934 0 0 0 0   .13725251   .05253892
1571  -.06209624424128384 1 0 0 0   .43546695   .10759732
1572  .049678341498111456 0 0 0 0  -.06209625   .09911264
1573  -.06210395816638141 0 0 0 0   .04967834   .09675863
1574  -.13675765594977138 0 0 0 0  -.06210396   .09319783
1575   -.7868610033383301 0 0 0 0  -.13675766    .0951393
1578    -.502831989732509 1 0 0 0    -.786861   .03523344
1579    .6907456035888876 0 0 0 0    -.502832  .009611278
1580   -.2506329648503502 0 0 0 0    .6907456   .04057193
1581   -.3015810353509959 0 0 0 1  -.25063297   .03205057
1582    .8895617306367889 0 0 1 1    -.301581   .02754111
1585   .37351014771604624 1 0 1 1    .8895617  .014364884
1586    .5082081035194379 0 0 1 1   .37351015   .03146704
1587   .22230589068534296 0 0 1 0    .5082081   .05313709
1588    .1109722079237272 0 0 1 0    .2223059   .05869559
1589   -.1850163933878988 0 0 1 0    .1109722   .07967273
1592  -.12353058861142528 1 0 1 0   -.1850164  .071496524
1593    .3208715456650392 0 0 1 0   -.1235306   .06220952
1594  -.23438361946989042 0 0 1 0    .3208715   .07396688
1595  -.13594514685972198 0 0 1 0   -.2343836   .06786942
1596   .29636598807756503 0 0 1 0  -.13594514   .04917125
1599   -.4696548026597588 1 0 1 0   .29636598  .034023948
1600   -.5216730121241245 0 0 1 0   -.4696548  .010039246
1601   .44731807234804744 0 0 1 0    -.521673 -.014129493
1602    .3465325121284463 0 0 1 0    .4473181  .009025703
1603    -.259787358955048 0 0 1 0    .3465325  .022519074
end
format %tdnn/dd/CCYY Date

After reading several threads in this forum, I guess the code will be something like

gen pred_ret = .

forval i = 1964/2019 {

    regress SP500 DMon DJan DToM DSummer lag1 movavmonth if year=`i'

    predict temp

    replace pred_ret = temp if year == `i'

    drop temp

}

Maybe I will also have to include some "local start" and "local end" values? I really don't know and I have no idea how to tell the loop that it should use a 10 year interval for the regression, predict the daily returns for the coming year and use another (one year forward) 10 year interval to predict the next year.
I really hope this was relatively clear and would appreciate any help!!
Thank you.

Kind regards,
Jannis

[Jannis Schmidt]

I think I came up with the solution myself:

gen pred_ret = .
forval i = 1964/2019 {
regress SP500 DMon DJan DToM DSummer lag1 if inrange(year,`i',`i'+10)
predict temp
replace pred_ret = temp if year == `i'+11
drop temp
}

[William Lisowski]

I think it is possible you have made a common mistake in your code in post #2.

In post #1 you wrote

I would like to run a regression on stock returns in the period of 1/1/1964 until 1/1/1974. ... So in the end I will have predicted returns until 2019 that are always based on the betas of a regression of the preceding 10 year period.

Now, if you constructed your year varaible as

year =yofd(Date)

then for the first time through the loop your regress command will be

regress SP500 DMon DJan DToM DSummer lag1 if inrange(year,1964,1974)

which will include Date values of 1/1/1964 until 12/31/1974, an 11-year period.

I think that you would more correctly say

I would like to run a regression on stock returns in the period of 1/1/1964 until 12/31/1973.

and then in your code

regress SP500 DMon DJan DToM DSummer lag1 if inrange(year,`i',`i'+9)
predict temp
replace pred_ret = temp if year == `i'+10

[Jannis Schmidt]

Hello William,
you're completely right. Thanks a lot for your help, I would not have realized this mistake!

Kind regards,
Jannis