中国股市收益率与波动性长记忆性的实证研究

200311:100026788(2003)01200092071,2,3,4(1.,610031;2.,610041;3.,610065;4.,100080):Granger,L:,;;L:;;;:F830.91:ATheEmpiricalAnalysisoftheLongMemoryPropertiesofStockMarketReturnsandVolatilitiesinChinaLIYa2jing1,2,HEYue3,ZHUHong2quan4(1.CollegeofEconomicsandManagement,SouthwestJiaotongUniversity,Chengdu610031,China;2.DepartmentofComputerScienceandEngineering,SouthwestNationalCollege,Chengdu610041,China;3.DepartmentofManagementScienceandEngineering,SichuanUniversity,Chengdu610065,China;4.InstituteofSystemsScience,AcademyofMath2ematicsandSystemsSciences,ChineseAcademyofSciences,Beijing100080,China)Abstract:ByGranger’sconceptoflongmemoryonseriesthispaperanalyzesthelongmemoryproper2tiesofstockmarketabsolutereturnsandvolatilitiesinChina.TheresultsshowthatthestockmarketreturnsandvolatilitiesinChinahavelongmemoryandpersistencealthoughtheyarenotasstrongasthatofAmericanstockmarket;ThememoryofShanghaistockisstrongerthanthatofShenzhenstock;Theautocorrelationfunctionofafractionalintegrationmodelcanfitthesampleautocorrelationmuchwell.Keywords:return;volatility;autocorrelation;longmemory:2001206229:(79930900):(1964-),,,,,:1,,rtZ,Taylor[1],{ûrtû},,ZDing[2-4]500,,{ûrtûd},d0;d=1,{ûrtûd}2500,(longmemory)Z,,,L,(volatilityclustering)(persistence),t,L©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,,;,,,L,L[2,3,4],,L,:19918199912,2071;19926200010,2078;2058Lrt(rt=lnPt-lnPt-1,Ptt)L;,;,,;L2Granger[4],{hj},j=0,1,2,,,:ht(B)=6tj=0hjBj,BZ{et}:et=m+Et,EtR20,corr(Et,Es)=0,tsZ{et}{xt},xt=ht(B)etZ:m(t)=mht(1),v(t)=R206tj=0h2j,s(t)=6tj=0hjEt-jfN(X)=EN-16Nt=0steitX2(1)XE0,f(X)=limNsteitX,f(X)xtZht(1),m(t)v(t)xtZ{xt},:1)f(X)X0;2)X,f(X)ZX,f(X)Z1),{hj}Zhj=Ad-1j,I(d)[5]ZX,X-2dZd,[5](fractionalintegrationprocess)ZARMA(hjHj,ûHû1),,tEtxt+kZ3,,,ZDing[2]500,rt,{ûrtû},2500,Z1rt,ûrtûr2tZ1,rt,ûrtûr2t,100(r2t)Zûrtû,200,Z,,ûrtûr2tûrtûr2t,Z1Z0120031©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.11234510204060100rt0.031-0.0200.089-0.072-0.0200.0130.0590.0030.054-0.027ûrtû0.3010.2510.2970.2580.2410.1640.1390.1620.0850.054r2t0.3850.1810.2650.2550.1560.0790.0500.0690.0160.022rt0.0240.0340.0680.0320.042-0.025-0.0240.002-0.002-0.032ûrtû0.3190.3610.3050.2640.1830.2000.1830.1100.1610.057r2t0.1430.3040.2180.1890.0720.0700.0560.0260.0330.002rt0.0330.0450.0260.0500.051-0.0410.0500.0130.004-0.017ûrtû0.2810.3170.2410.2050.1900.1200.1270.0430.0830.005r2t0.1250.2090.2110.0870.0720.0330.059-0.0050.030-0.0151,rt,rt5,Zrt,,Z5,Z,ZZ,Z{rt},rt,{ûrtû}{r2t},0Z11{ûrtû}{r2t}Z{rt}Z1ûrtûrt()1ûrtûrtZ,rt,N(0,1öT)Z(1.96öT,T)95%Z1,,200301.96öT,10Zrtûrtûd,d,ûrtûd,80Z,2Z3d,ûrtûdZ3,ûrtûd100Z,ûrtû200Z,ûrtûZ111©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2ûrrûd()d12345102040601000.1250.2530.2330.2360.2350.2010.1980.1810.0970.1360.0770.250.2820.2650.2600.2520.2110.2140.1960.1100.1480.0820.50.3220.3150.2940.2700.2180.2290.2100.1250.1650.0830.750.3340.3460.3080.2730.2070.2230.2050.1240.1690.07410.3190.3610.3050.2640.1830.2000.1830.1100.1610.0571.250.2830.3620.2900.2480.1530.1660.1520.0880.1430.0391.50.2360.3500.2680.2280.1220.1300.1160.0630.1190.0221.750.1870.3300.2430.2080.0950.0970.0830.0420.0950.01020.1430.3040.2180.1890.0720.0700.0560.0260.0330.00230.0410.1970.1310.1320.0240.0170.0070.0000.020-0.0053ûrtûdd0.1250.250.50.7511.251.51.752310410412312312312310310310322212212212214208176107107951575758178787850424092d,,d1,,d,Z2,2ûrtûd125dZ22dZd,,,d,Z125d0.75,10.5Zd,2Z2ûrtû125d1,rt,95àZûrtû,,ûrtû100,15,Qk(ûrtû),Qk(ûrtû)ZARMAQk=ABkZ3Qk=ABkZûrtû15Z,(fractionalintegra2tionmodel)Z4ûrtû:Qk=#(1-d)#(d)3#(k+d)#(k+1-d)Z,d0.394,0.3590.378(),[6]Z4,(2120031©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.3ûrtû),Zd,Z4ûrtûQkd,,[6]ddZmind6200k=1[Qk(ûrtû)-Qk]2,d0.307,0.3030.256,4Z,Z4,,Z,,,Z[7-11],,[12-15],[10,11,16],L[16-18](ARCHGARCH)L,L:rt=65i=1AiDit+612j=1Bjrt-j+Lt(2),rt,Lt,DitZi=1,t,Dit1,0ZZAiBjZ,(2)ûLtû,Z,Z,{ûLtû}115,21378ZZ,Z,,311©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.;,,,1994Z,Z,,;,,Zd0.382,0.3840.372;mind6200k=1[Qk(ûLtû)-Qk]2d0.298,0.3010.246Z5ûLtû5{ûLtû}Z{ûrtû}Z,[6]d,(),Z,mind6200k=1[Qk(ûLtû)-Qk]2dZ5Granger,Z:{rt},Z,;{rt}{ûrtûd},d0Zd,ûrtûd100Z,ûrtû200,;{ûrtûd},d0,,;Z{ûLtû},213,Z;:[1]TaylorS.ModellingFinancialTimeSeries[M].NewYork:JohnWiley&Sons,1986.[2]ZhuanxinDing,CliveWJGranger,RobertFEngle.alongmemorypropertyofstockmarketreturnsandanewmodel[J].JournalofEmpiricalFinance,1993,1(1):83-106.[3]ZhuanxinDing,CliveWJGranger.Modellingvolatilitypersistenceofspeculativereturns:anewapproach[J].JournalofEconometrics,1996,73:185-215.4120031©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.[4]CliveWJGranger,ZhuanxinDing.Varietiesoflongmemorymodels[J].JournalofEconometrics,1996,73:61-77.[5]GrangerCWJ,JoyeuxR.Anintroductiontolong2memorytimeseriesmodelsandfractionaldifferencing[J].Jour2nalofTimeSeriesAnalysis,1980,1:15-29.[6]GewekeJ,AnsS.Porter2Hudak.Theestimationandapplicationoflongmemorytimeseriesmodels[J].JournalofTimeSeriesAnalysis,1983,(4):221-238.[7]KeimBD,StambaughRF.Afurtherinvestigationoftheweekendeffectinstockre