我需要根据Boyer, B.H., Mitton, T. and Vorkink, K. (2010), “Expected idiosyncratic skewness”, The review of financial studies, Vol. 23 No. 1, pp. 169–202.的文章计算期望特质偏度( expected idiosyncratic skewness),在中间的某一个计算历史特质波动率和偏度( historical estimates of idiosyncratic volatility and skewness)的步骤遇到了问题。
先简短描述一下我的问题:
在每个月t,我需要做以下计算/分析:
1. 首先对t-2到t月的数据进行FamaFrench三因子回归分析,公式是excessreturn = b_cons + b_hml*hml + b_smb*smb + b_rmrf*rmrf,得出回归系数b_cons、b_hml、b_smb、b_rmrf。
2. 用步骤1得出的回归系数计算t-2到t月的残差。
3. 用2中的残差计算t月特质波动率(sd)和偏度(skewness)。
4.下一个月进行以上同样的步骤。
5. 我有很多公司,我的数据是时间序列数据:一共有5888个变量9262观察值,变量是date(日期) ym(年月) rmrf(解释变量) smb(解释变量) hml(解释变量) excessreturn1-excessreturn5883(5883个公司的额外回报);时间是从1981年1月1日到2016年6月30日。我没有转换成面板资料,因为电脑系统是32位的,转换之后数据就有近2G,再做运算就会内存不足。我自己是用foreach c of varlist excessreturn1-excessreturn5883{}命令做循环的,比较笨也比较慢。您也可以把我这个数据当成面板数据处理,如果有运算思路也可以告诉我,谢谢。
6. 每个月我只想得到一个值,或者说上面问题中的sd的值和skewness的值各一个。
举个例子,在1989年1月,我需要对1988年11月到1989年1月的数据进行回归,得到一组回归系数。用这组回归系数计算1988年11月到1989年1月的残差。然后计算分别得出一个残差的sd和skewness。在1989年2月,我需要对1988年12月到1989年2月的数据进行回归,得到一组回归系数。用这组回归系数计算1988年12月到1989年2月的残差。然后计算分别得出一个残差的sd和skewness。以此类推。
我先贴上我自己写的命令,我的问题是,其中计算残差的那步是有错误的,我只是用t月的回归系数计算了t月残差,实际应该计算前3个月的残差。也可能我这里用rangestat不太合适。另外我的数据一共有几百个月,所以不能手动一次次计算。
- rangestat (reg) excessreturn rmrf smb hml, interval(ym -2 0)
- gen Resid= excessreturn - b_cons - b_hml*hml - b_smb*smb - b_rmrf*rmrf
- rangestat (sd) IV=Resid, int(ym -2 0)
- rangestat (skewness) IS=Resid, int(ym -2 0)
下面是样本数据
- * Example generated by -dataex-. To install: ssc install dataex
- clear
- input double(date ym excessreturn rmrf smb hml)
- 10503 345 -.01936289646965491 -.01127306 .00525148 .0006878
- 10504 345 .004428615495805104 .00170627 -.00085576 -.00139754
- 10505 345 -.0004251 .00996818 -.00446347 .00140606
- 10506 345 -.0004254 .0059196 -.00249881 .00250139
- 10507 345 -.0004254 .00319251 .00030991 -.00277563
- 10510 345 -.0004223 -.00024731 .00422974 -.00149079
- 10511 345 -.0004216 -.00274863 .00377518 .00549557
- 10512 345 -.0004223 -.01161097 .00538493 .00050242
- 10513 345 -.0004223 .00748774 -.00172834 .00512555
- 10514 345 -.0004223 .00450467 -.00003376 .00478568
- 10517 345 .023616446896690534 .01022073 -.00470417 .00443819
- 10518 345 .013620751277013725 -.0011541 .00067627 -.00090353
- 10519 345 .013474597771965517 .00363072 .00327984 -.00298672
- 10520 345 -.0004251 .00043836 -.00042181 .00095446
- 10521 345 .004160660287584015 -.00152961 .0025553 .0011501
- 10524 345 .004094270973417762 -.00565686 .00289626 -.00235665
- 10525 345 -.00491995430789627 -.00111718 -.00253788 .00240047
- 10526 345 -.0004223 .00032483 -.0014962 .00228125
- 10527 345 .017744790651005753 .00044753 .00076314 .00001995
- 10528 345 .008496248264910458 .00309713 .00082262 .00215505
- 10531 345 -.0004216 -.00123408 .00574452 .00172679
- 10532 346 -.0004251 .00287933 -.00061362 .00232
- 10533 346 -.0004233 -.00697585 .00488589 .00050676
- 10534 346 -.0004244 -.00285437 .00281202 .0029033
- 10535 346 .004018632959910915 -.00192175 .0009521 .00358065
- 10538 346 -.0004254 -.00776155 .0027741 .00311697
- 10539 346 -.0004264 .00952688 -.00659687 .00322087
- 10540 346 -.0004254 -.00755174 .00424434 .00203433
- 10541 346 -.0004244 .0000658 -.00040594 .00213749
- 10542 346 -.0004227 -.01219847 .00586826 .00206838
- 10545 346 -.013649725532307035 -.00454815 -.00256307 .00250378
- 10546 346 -.0004233 .00395039 .00248942 .00142837
- 10547 346 -.0004213 .00237563 -.00113014 .00247123
- 10548 346 -.0004223 .00695646 -.00743721 -.00091841
- 10549 346 -.0004244 -.00040684 .00169483 .00343632
- 10552 346 .004060976614823962 -.00631036 .00254483 -.00003972
- 10553 346 -.004886662993443917 .00421284 -.00169779 .00349698
- 10554 346 -.000424 .00715559 -.00209694 .00426515
- 10555 346 -.004908076614824184 -.00287966 .0015931 .00042118
- 10556 346 -.013841080905465748 -.02226113 .00126729 -.00038323
- 10559 346 -.0004548 -.00686149 .00134545 .00068337
- 10560 346 -.0050233243520851146 .00304422 -.00087426 -.00150591
- 10561 346 -.0004606 .00311911 .00006603 .00334213
- 10562 347 -.005045560287584237 -.00880611 -.00284232 .00227736
- 10563 347 -.005018397581225804 -.00939757 -.00306623 -.00021765
- 10566 347 -.0004585 -.00323499 -.00183136 .00373087
- 10567 347 -.00966786949185222 .00212448 -.00235887 .00124775
- 10568 347 -.005130805532577441 .00061133 -.00497766 -.0044441
- 10569 347 -.005102141236861527 -.00950524 -.00064092 .00103131
- 10570 347 -.005172627701375276 -.00722724 -.00339905 .00152378
- 10573 347 -.005192565455980971 .00015278 -.00530367 -.00236584
- 10574 347 -.0004548 .00223309 .00088146 .00437897
- 10575 347 -.005164832368107975 -.00032592 -.00276482 .00010165
- 10576 347 -.0004575 .00387507 -.00047641 -.00151807
- 10577 347 .00905806926717472 .00552013 -.00129807 .00101304
- 10580 347 -.005191265455980971 -.00128961 -7.196e-06 .00584483
- 10581 347 -.0004544 .00347369 -.0033825 -.00407795
- 10582 347 -.0004565 -.00266647 -.00067593 -.00204654
- 10583 347 -.0004551 -.00176227 .0036615 -.00504651
- 10584 347 -.0004517 .00185695 -.00313413 .00019805
- 10589 347 -.0004521 .00926918 -.00593432 -.00186907
- 10590 347 -.0004534 .00813243 -.00295587 -.00200299
- 10591 347 -.0004575 -.00457141 .00446324 .00128521
- 10595 348 -.0004603 -.00625428 .00348006 .00297693
- 10596 348 -.009930748234827456 .00525955 -.0027392 -.00272645
- 10597 348 -.0004603 .00329548 -.00122743 -.00069683
- 10598 348 .009101095144415997 .00577624 -.00208543 -.00008884
- 10601 348 -.0004593 .0099526 -.00551761 -.00026279
- 10602 348 .009059031733438961 .00179973 .00354946 .00461995
- 10603 348 -.0004603 -.00075754 .00440392 .00339012
- 10604 348 -.0004593 .00819852 -.00007103 .00246756
- 10605 348 -.0004593 .0060607 .0023039 -.00229719
- 10608 348 .004205411787819446 .00513847 -.00015631 .00334099
- 10609 348 -.0004613 -.00229445 .00057371 -.00277521
- 10610 348 -.0004613 .01093528 -.00588377 -.00158704
- 10611 348 .027600298631141437 .00921167 -.00284583 -.00459487
- 10612 348 -.0004613 .00313551 -.00084835 -.00063124
- 10615 348 .013138266298920526 .00374158 .00260237 -.00339525
- 10616 348 -.0004623 .00752605 -.00519193 .00170633
- 10617 348 -.0004617 -.00090837 .00317521 .00025433
- 10618 348 -.0004613 .00960258 -.00631583 .0045522
- 10619 348 .008546441027445393 .02269427 -.00559572 -.00016106
- 10622 348 .07504929897242767 .01651668 -.00309322 -.00189771
- 10623 348 -.0004613 .00320827 -.0016308 .00090841
- 10624 349 -.0004603 -.0049795 .00361908 -.00676923
- 10625 349 -.004567342497081826 .00225093 .00262478 .00050828
- 10626 349 -.0004599 .01362544 -.0009618 .00026414
- 10629 349 -.0004603 -.01070708 .00748479 -.00392056
- 10630 349 -.0004613 .01264815 -.00663474 -.00156815
- 10631 349 .003662679857614035 .0107934 -.00043577 .00168113
- 10632 349 -.0004613 -.00688215 .00523801 .00368968
- 10633 349 -.004567342497081826 -.01046152 .00620448 .00326649
- 10636 349 -.004626690171904928 -.01071695 .00314722 -.00381311
- 10637 349 -.0004593 .00668561 -.00352879 .00087794
- 10638 349 -.0004596 -.00106768 .00325114 .0002309
- 10639 349 .0037255299912816687 -.0052176 .00625345 -.00239602
- 10640 349 -.008750670029519073 .00303642 -.00170061 -.00133237
- 10643 349 -.0004579 .00946149 -.00533087 .00049292
- 10644 349 -.0004572 -.00169463 .00397498 .00187004
- 10645 349 -.004658732435981501 -.01182387 .00857389 .00020951
- end
- format %td date
- format %tm ym