Dear All

I had an old post that perhaps was not clear. As is advised by some of you, I decided to create a new one that is more to the point.

I want to estimate out-of-sample forecasts for a variable called BUS using predictors s1-s5.
I have nearly 500 predictors but I try to simplify the issue here by showing only 5 predictors.

As you see from the data structure below, BUS is a quarterly variable but s1-s5 are weekly variables (i.e. BUS is updated on a quarterly basis while s1-s5 are updated every week).
My aim is to run a lasso regression every week and make an out-of-sample prediction for the quarterly variable BUS. These out-of-sample predictions are then updated every week when new observations of s1-s5 become available. Ultimately, I want to see whether the out-of-sample predictions become more accurate throughout the quarter (i.e. from week 1 to week 12 of the quarter).

The variable "series" takes value 1 to 12 consistent with the weeks (i.e. series=1 is for weekly data available at week 1, series=2 is for weekly data available at week 2, etc.)

I think I managed to make predictions but I believe they are in-sample predictions as follows:

Code:
gen prediction=.

levelsof series, local(levels)

foreach x of local levels {
  
lasso linear BUS s1 s2 s3 s4 s5 if series==`x' 
predict temp if series==`x', postselection
replace prediction=temp  if series==`x' 
drop temp
}

The problem is that I am not sure how to make these predictions out-of-sample? More specifically, the business cycle analyst can see the predictors s1-s5 in real-time as at week 1 for example but can not see the quarterly variable BUS in real-time as it is only available at the end of the quarter. Therefore, I want to estimate the parameters of the model using data from weeks 1 up till (and without) data from week 1 of the current quarter and then use the predictors in week 1 of the current quarter to make the forecast out-of-sample. Similarly, I want to estimate the parameters of the model using data from weeks 2 up till (and without) data from week2 of the current quarter and then use the predictors in week 2 of the current quarter to make the forecast out-of-sample, and so on.

Here is an example of my time-series data


Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input float(BUS s1 s2 s3 s4 s5 series) int year byte(quarter month week) float quarter_date
 5.28   1.4280612 -1.7400645  2.1785972    .6041555           0 1 1987 1 1 1 108
 7.32   -.3261277 -2.8215795 -.23142336    7.937459    .3825918 1 1987 2 1 1 109
 6.13     .706113 -3.8739974   1.460365    .1957696   .24385256 1 1987 3 1 1 110
 9.83    .4272946  -3.122698  1.1591737    2.161951    .3692954 1 1987 4 1 1 111
 5.02    1.432191 -3.5722666   2.432849    .5817058           0 1 1988 1 1 1 112
 9.75   .17579167  -1.486287  1.0115452   1.0553348   .28939685 1 1988 2 1 1 113
 7.31    1.411383   -3.54055  1.7815936 -.020459617     .610453 1 1988 3 1 1 114
 8.85    1.715589 -1.0885705   2.654196    .3305015           0 1 1988 4 1 1 115
 9.04   1.8187963  -2.506453   2.738661    .4680699           0 1 1989 1 1 1 116
 7.42   1.8606597  -2.459989    2.78734    .3364668           0 1 1989 2 1 1 117
 5.51    1.887378  1.6824546   2.860331    .0734062           0 1 1989 3 1 1 118
 2.54    1.911596  2.3742833   2.920467   .09255037           0 1 1989 4 1 1 119
 9.35   .36569595   .9221073  1.4366348    .6418874   .25642812 1 1990 1 1 1 120
 4.82   2.0296164 -1.8166744  3.0796354    .0996016           0 1 1990 2 1 1 121
 2.53   2.0968032  1.9894003   3.134805   .18245694           0 1 1990 3 1 1 122
-2.42    3.010042  4.6542344  4.4679475    5.588562   .10877172 1 1990 4 1 1 123
  .49    3.114446   7.097381   3.351834    .7527507   -.0597137 1 1991 1 1 1 124
 6.31    3.216622   9.544506   6.088016    7.100855  -.11968945 1 1991 2 1 1 125
 5.17   4.0031595   5.090754   4.819216    .7430318 -.064995535 1 1991 3 1 1 126
 3.06   1.7156185  -.3905046  1.8559965   -.3724067    .1004606 1 1991 4 1 1 127
 6.93   1.9902998  1.9397452  2.1061885   -.7137325   .14847873 1 1992 1 1 1 128
 6.95    2.597939   2.390985   .7381327   -4.080062    .5012339 1 1992 2 1 1 129
 6.33   1.6087084 -1.3339542  1.9718102    .5833408   .14864297 1 1992 3 1 1 130
 7.74   1.7855448   .8567627   1.962867    .7399028   .26191464 1 1992 4 1 1 131
 5.28    -.312875 -2.0297842  -.6567536    .7758612    .4881686 2 1987 1 1 2 108
 7.32  -1.5230926  -2.703133 -3.0387714    2.954472   .22246388 2 1987 2 1 2 109
 6.13   -.6086997 -3.5352764 -1.9099023  .026646543    .2183693 2 1987 3 1 2 110
 9.83  -1.0030841  -3.710979  -.8193175   1.0371368    .2992593 2 1987 4 1 2 111
 5.02   -1.315071  -5.708353   -1.81234    .5035552   .23610453 2 1988 1 1 2 112
 9.75   -.6764717 -1.3538846 -2.5990624    -.758627    .1763391 2 1988 2 1 2 113
 7.31  -.21421558 -2.4105334  .40100315   1.1111029   .23137583 2 1988 3 1 2 114
 8.85  -.49769095 -.08228127  1.0387636    .5207426    .1803996 2 1988 4 1 2 115
 9.04 -.014957066 -1.9950553 -.58217704    .8293411   .22317313 2 1989 1 1 2 116
 7.42   -.8647903  -.7270581  -.8096528     .901518    .1744625 2 1989 2 1 2 117
 5.51    .8862366  2.6689715  1.2430537  -.29651818   .16048166 2 1989 3 1 2 118
 2.54   .05685891   3.506664  -.1775705  -1.1541252   .20539308 2 1989 4 1 2 119
 9.35  -1.5025678   .8159853 -1.1917896   -.5318023   .11380605 2 1990 1 1 2 120
 4.82   1.5260097 -1.1706387  -.9492483   .24037273   .15399224 2 1990 2 1 2 121
 2.53    .9257024  -.4118942   .7638614  -2.0135093   .15347226 2 1990 3 1 2 122
-2.42   1.1741554  1.1157335   .8788975    .4426497    .1168849 2 1990 4 1 2 123
  .49    3.525193   6.711821   5.894926   2.0596566   -.1692952 2 1991 1 1 2 124
 6.31   4.2774143   8.058287   9.068833   1.0657045   -.1169197 2 1991 2 1 2 125
 5.17    3.225771   .4149646   5.304836  -.31201684  -.10806065 2 1991 3 1 2 126
 3.06    .6311643  -2.970027 -.28448343  -.07355707   .15270847 2 1991 4 1 2 127
 6.93    .8370029   .5811588   -.950491    2.069583   .11863983 2 1992 1 1 2 128
 6.95    .8845069  1.4056878 -1.5377135   -.4812104     .114008 2 1992 2 1 2 129
 6.33   .51111126 -4.1659355 -1.9837395   .09373852    .3755253 2 1992 3 1 2 130
 7.74   -.3481121 -1.0498939  -.3189843  .066026814   .10963735 2 1992 4 1 2 131
 5.28   -2.356725 -2.1076612 -2.7361324    .2479541   .22487326 3 1987 1 1 3 108
 7.32  -2.2176385   -2.59371  -3.308432   -.8266953   .13695842 3 1987 2 1 3 109
 6.13   -1.988106 -3.5369556 -2.5531945   1.8277788    .1750264 3 1987 3 1 3 110
 9.83  -1.8028708  -3.756836  -2.467215   1.5251398    .1382897 3 1987 4 1 3 111
 5.02    -1.60548  -5.638969 -2.2708828   .28224888    .2874467 3 1988 1 1 3 112
 9.75  -2.2246215 -1.3491007 -1.7797307   .06242354   .13456556 3 1988 2 1 3 113
 7.31   -2.578337  -2.410444 -1.8754367   1.4670404   .12353268 3 1988 3 1 3 114
 8.85   -.7692303 -.09574382 -1.9727464    .4673429   .11508931 3 1988 4 1 3 115
 9.04   -.9678542  -1.995568 -1.9843154   -.5841132   .29625088 3 1989 1 1 3 116
 7.42   -.6068677  -.6276433  -2.032895   -.3696545   .12134252 3 1989 2 1 3 117
 5.51  -.12857853   2.771389 -1.5378385     .317264   .11938269 3 1989 3 1 3 118
 2.54  -1.0707742   3.595633  -2.094334  .035563562    .1235524 3 1989 4 1 3 119
 9.35    -.970474   .8063396 -1.1299096    .6624953   .13118356 3 1990 1 1 3 120
 4.82    .2601256 -1.0888479 -1.6639595    .6947708    .1191846 3 1990 2 1 3 121
 2.53   .30467215 -.40419185 -1.7502427  -.43394426    .1235137 3 1990 3 1 3 122
-2.42    .9444076  1.1760539  -.2948909    .7812307   .13087627 3 1990 4 1 3 123
  .49   3.9914865   6.568848   6.704494    1.595678   -.1509655 3 1991 1 1 3 124
 6.31    5.012939   7.920979   8.347696  -.54813856  -.12451165 3 1991 2 1 3 125
 5.17    5.038057   .3071753    7.27375   -.9620001  -.11965105 3 1991 3 1 3 126
 3.06   1.2079372  -3.035961  -.2178535  -.05455993   .15887807 3 1991 4 1 3 127
 6.93   .06978367   .6693566  -.8070132   1.7806284   .14646508 3 1992 1 1 3 128
 6.95   -.1376001  1.3361707 -1.2892662   .38877955    .1481647 3 1992 2 1 3 129
 6.33   -.6247261 -4.2310996 -1.1468972    .3107327   .13287802 3 1992 3 1 3 130
 7.74  -1.0327399 -1.0610285 -1.2286204    .1454983   .15739937 3 1992 4 1 3 131
 5.28  -1.0315892 -1.9988308 -2.6316936    .6735969   .13540626 4 1987 1 1 4 108
 7.32   -.9939098  -2.511362   -2.58485    .4599007   .15181194 4 1987 2 1 4 109
 6.13  -1.5999373 -3.6620574  -2.831921    1.808131   .20369446 4 1987 3 1 4 110
 9.83  -2.7039974  -3.832227  -3.109755   1.0882541    .1632594 4 1987 4 1 4 111
 5.02   -3.543656  -5.493874 -2.1929116   1.3907964    .1679988 4 1988 1 1 4 112
 9.75  -1.9179015 -1.2556508  -2.625051   1.0341737    .1740451 4 1988 2 1 4 113
 7.31   -1.778265  -2.495931 -2.4760535   1.4696044   .17356914 4 1988 3 1 4 114
 8.85  -1.2345937 -.22844014  -2.127411   1.1983488   .15559915 4 1988 4 1 4 115
 9.04   -.9724296 -2.0516148 -2.1667652    .8662595   .14979433 4 1989 1 1 4 116
 7.42  -1.5865642  -.7517704  -1.934539 -.001189246   .15478706 4 1989 2 1 4 117
 5.51   -1.353096   2.647187 -1.8039092  -.07529771   .15468076 4 1989 3 1 4 118
 2.54   -.4403289  3.6720455 -1.8033653   .14847729     .158337 4 1989 4 1 4 119
 9.35   -.7641429   .8248587 -1.5446472    .3296993   .13763453 4 1990 1 1 4 120
 4.82   -.3110338  -1.201032 -1.2366627  .017878672   .14217184 4 1990 2 1 4 121
 2.53   -.0579773 -.37944755 -1.5019845   .16272673   .14685132 4 1990 3 1 4 122
-2.42     .551628  1.1874413  -.4475872   1.1742166    .1394521 4 1990 4 1 4 123
  .49   3.9375834   6.587499   7.437414    .2495805   -.1574398 4 1991 1 1 4 124
 6.31   4.6535735   8.093565   8.163906   -.8019937  -.13311808 4 1991 2 1 4 125
 5.17    4.676563   .3106449   6.918107   -.8722724   -.1107249 4 1991 3 1 4 126
 3.06    1.301191  -2.932334  -.5840098  -.06370235     .166544 4 1991 4 1 4 127
 6.93  -.06733606   .9889328  -1.319969    .2210396   .14780125 4 1992 1 1 4 128
 6.95  -.25309724   1.299411 -1.0797026    .2594811    .1547733 4 1992 2 1 4 129
 6.33    -.437004 -4.1473575 -1.1806424    .2261984   .18456896 4 1992 3 1 4 130
 7.74   -.8715544  -.8834404 -1.0527567   .24967523   .16514884 4 1992 4 1 4 131
 5.28  -1.0928361 -2.1836462 -2.6183126    .8119413   .13540626 5 1987 1 2 1 108
 7.32   -.9907247   -3.33188  -2.753484    .6022525    .1520763 5 1987 2 2 1 109
 6.13  -1.7747288  -3.991014  -2.996839    2.509792    .2036956 5 1987 3 2 1 110
 9.83  -3.0593615  -3.507675  -3.167567   1.2470064    .1632594 5 1987 4 2 1 111
end
format %tq quarter_date