混合数据抽样波动模型

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.()(MIDAS)MIDASABDL,,ABDLMIDAS;MIDAS,;MIDAS,MIDASABDLBetaF22410AMixedDataSamplingVolatilityModelAbstract:ThispapercomparesMIDAS(MixedDataSampling)regressionmodelsandABDLmodelintheabilityofpredictingvolatility1MIDASmodelscantakedifferentspecificationofregressors,suchasrealizedvolatility,realizedpower,squaredreturns,absolutereturns,andreturnranges1Using52minutestockreturndatainShanghaiandShenzhenStockExchange,wefindMIDASmodelsdonotexcelABDLmodelinpre2dictingvolatility1However,measuredbyincrementsinquadraticvariation,dailyabsolutereturnisthebestpredictorinMIDASmodels1Furthermore,historicalda2taofonemontharesufficienttocapturethepersistenceinvolatility1Keywords:MIDASVolatilityModel;ABDLModel;BetaFunction,Engle(1982),Engle(1982)Bollerslev(1986)ARCH/GARCH,rt22t+1|t=A(L)rt2,(MIDAS);,,Ding,GrangerEngle(1993)ForsbergGhysels(2004)77(70573025)©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.|rt|,Alizadeh,BrandtDiebold(2002)(-)AndersenBollerslev(1998),(530),Andersen,Bollerslev,DieboldLabys(ABDL,2003)(ARFI),ABDLARCH;Ghysels,Santa2ClaraValkanov(2006)MIDASABDL,(realizedpower)20013120059305,Ghysels,Santa2ClaraValkanov(20042005),,ABDLMIDASHMIDASABDL5H(Vt+H,t)9:3011:301:003:00,4,485,485t5rt,t-1/48=log(Pt)-log(Pt-1/48)H(Vt+H,t)AndersenBollerslev(1998),RVt+H,t,1(H=5)4(H=20),,,m,H:RV(Hm)t+H,t=Hmj=0rt+H-(j-1)/m,t+H-(j-2)/m2(1)MIDASMIDAS:V(Hm)t+H,t=H+HJj=0BH(j,)Y(m)t-j,t-j-1+Ht(1),V(Hm)t+H,tH,RV(Hm)t+H,tlogRV(Hm)t+H,t;Y(m)t-j,t-j-1,,(m=1)5(m=48)(m=240)BH,,(parameterproliferation)H1234,,5,5,m=48MIDAS,,Y(m)t-j,t-j-1V(Hm)t+H,t(2)Beta(1)BH,MIDAS87200711Andersen,Bollerslev,DieboldLabys(2001),,©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(1)HY(m)t-j,t-j-1RV(Hm)t+H,t,AlmonBeta(Ghysels,SinkoValkanov,2005)(Anderson,GhyselsJuergens,2005)Beta,=[1;2],:BH(j,1,2)=g(j/J,1,2)Jj=1g(j/J,1,2)g(z,,)=z-1(1-z)-1/(,)(,)=/+(2),()=0e-xx-1dxBetaBeta,1=121,;211,(,2005);1=2=1,(3)Y(m)t-j,t-j-1,RV(m)t+1,t=mj=0rt+1-(j-1)/m,t+1-(j-2)/m2ŽP(m)t+1,t=mj=0rt+1-(j-1)/m,t+1-(j-2)/mr2|r|(hi-lo)5MIDAS:RV(Hm)t+H,t=RVH+RVHJj=0BRVH(j,)RV(m)t-j,t-j-1+RVHt(3)RV(Hm)t+H,t=PH+PHJj=0BPH(j,)ŽP(m)t-j,t-j-1+PHt(4)RV(Hm)t+H,t=VH+VHJj=0BVH(j,)rt-j,t-j-12+VHt(5)RV(Hm)t+H,t=aH+aHJj=0BaH(j,)rt-j,t-j-1+aHt(6)RV(Hm)t+H,t=rH+rHJj=0BrH(j,)hi-lot-j,t-j-1+rHt(7)(3)H(Andersen,Bollerslev,DieboldLabys,2003)(4),,(Barndorff2NielsenShephard,20032004)(5),ARCH(6)(7)(3)(7),ABDL(4)ABDLAndersen,Bollerslev,DieboldLabys(2003)ARFI(5,d),,ABDLARCHAB2DL:97©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=1cjLj1-LdlogRV(m)t+1,t=+t(8),(8),dABDL6()MIDASABDL:MIDAS,ABDL,ARCH;BetaMI2DAS4,ABDL;,MIDASBeta,ABDLARFI;MIDASH,(H=5);ABDL,,MIDAS(5),Andersen,Bollerslev,DieboldLabys(2003),ABDLARCH,Ghysels,Santa2Clara,Valkanov(2006),MIDASABDL,MIDASAB2DL(MSE)MSEMIDAS/MSEABDL1,MIDASABDLMIADS,ABDL,,ABDL20013120059305,1AndersenBollerslev(1998)RV(m)t+1,t,1%,;(-3)1%,1RV(m)t+1,t010091010046115750331786031106010100010050118809351412331106:31%1RV(m)t+1,t180,10166801666,793208200711Robinson(1991),Ding,GrangerEngle(1993),Baillie,BollerslevMikkelsen(1996),BollerslevMikkelsen(1999),(2004),(2005)EGARCHR2200151117182120034295,5©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(m)t+1,t2logRV(m)t+1,tdGPHADF-418100147401033-010450144133-81773531106-4170401445012973011590127253-91949531106:31%,0101922log(RV(m)t+1,t),5%,;5%,1%,;5%,2180,10172801707,8039,2logRV(m)t+1,t2dGPH(GewekePorter2Hudak,1983)ADFdGPH014413012725,18©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2003)d01401,ARFI(5,d),ARCH,dARFI(5,d),014151013568,ABDL(2003)d01401,,MIDASABDL33ABDL(d=01401)c1c2c3c4c5-916896(1619)011020(314)010535(118)010443(115)010055(012)010608(210)-914685(1617)010789(216)010633(211)010249(018)010228(018)010621(211):NeweyWest(1987)t,14logRV(Hm)t+H,tMIDAS(2)Beta,J=50;,NeweyWest(1987)4MSEMIDAS/MSEABDL,MSEMIDASMIDASMSE,;MSEABDLABDL((8))MSEMIDAS14RV(Hm)t+H,tlogRV(Hm)t+H,t,42A42B4MIDASABDL:MSE4A:1115041135511428113031144911453114111140311324114532115921156111534115251163611631115921161411564116723117211168911770116511174711367113411140611311113884117861173611739117071178211833117861180811716118224B:111414114351141411414115201141711461115202116131168611592116171161311616116721165328200711©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.()4B:3117361176511731116761137711402113751133141182311803118101173111824118711194611789:,,4,,,MSEMIDAS/MSEABDL1,ABDL,MIDAS,Ghysels,SantaClaraValkanov(2006)MIDAS,,(14),MSEMIDAS/MSEABDL11303117071132411716,,MIDAS,,MIDAS34,,MSEMIDAS/MSEABDL11676117311133111789,12,,MSEMIDAS/MSEABDL;,MSEMIDAS/MSEABDL5,MIDAS,11,2525,,,H1%,14Q(15)Ljung2Box,1,Q(15)5%225,MIDAS,,MIDAS,1,2093%99%,62020%,,MIDAS,120013200595,MI2DASABDL,,ABDLMIDASMIDAS,;,1[1]:[J],2004