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1,1,2(1.,221008;2.,200052):,R/SBDS,.:;R/S;;BDS:F121.26:A:1007-9807(2004)05-0067-080[1](fractalmarkethypothesis,FMH),.,,,.,,,,.FMH(efficientmarkethypothesis,EMH),FMH,.(rescaledrangeanalysis,R/S),Peters[1,2]R/S.KwakuKOpong[3]R/SBDSFTSE.[4][5][6]R/S,[7].,Hurst.Peters[1]R/S,,R/S,.,BDS.11.1[8]Hurst,Hurst[8]Peter[1].(R/S)n=cnH(1):R;S;H(Hurstexponent);c;n.,log(R/S)n=log(c)+Hlogn(2),H,75200410JOURNALOFMANAGEMENTSCIENCESINCHINAVol.7No.5Oct.2004:2003-03-12;:2004-05-19.:(79970115).:(1974),,,..1.2R/S(independentidenticallydistributed,IID),,R/S.R/S,IID.,.,Hurst[8](R/S)n=(n3/2)0.5(3)Peters[1]IID,n(R/S)n(3);n,(3)Hurst.AnisLioyd[9]nR/S,E[(R/S)n],Peters[1],E[(R/S)n]=[(n-0.5)/n][(0.5(n-1))/((0.5n))]n-1r=1(n-r)/r(4),logE[(R/S)n]=log(c)+E(H)logn,HurstE(H).n,E[(R/S)n]Hurst,E(H)0.5;n,E[(R/S)n],E(H)0.5.Peter[1]HurstVr(H)=1/T.,E[(R/S)n](4).=H-E(H)Vr(H)N(0.1),.1.3VCVn=(R/S)n/n,Hurst[8],.(H=0.5),Vnlog(n).(H0.5),Vnlog(n).(H0.5),Vnlog(n).Vn,,.C=2(2H-1)-1,HHurst.IID,C=0;,0C1;,-0.5C0.1.4nR/STn,,,,.Peters[1]Tn,.,.,n,Hurst,n10.2,xt=ln(Pt)-ln(Pt-1),Pt.CMatlabEviews.2.11.1Table1DescriptivestatisticsofreturnsforShanghaistockmarketandShenzhenstockmarketSkewnessKurtosisJarque2Bera1990-12-192002-12-3029690.0008790.719152-0.1790510.0296475.756563129.712720026711990-12-192002-12-306080.0041460.900825-0.2262980.0726065.27404759.0038482274.871991-04-032003-01-2929330.0003840.232669-0.2442910.0253010.51341317.3743425379.751991-04-032003-01-295930.0018970.453813-0.2987710.0600641.54895115.178693901.881Jarque2Bera22.0.5%,10.6,.,.,Q-Q()1a,.862004101(a)Q-QFig.1(a)Q-Qplotforsampledistributionagainstnormaldistribution1(b)1(c).1(b),1(c)[2,6](),3.1(d)1(e),,,().Levy,,,,,..1(b)()Fig.1(b)Sampledensityfunction()1(c)()Fig.1(c)Sampledensityfunction()1(d)Fig.1(d)Meanofreturnswithincreasingdate1(e)Fig.1(e)Standarddeviationofreturnswithincreasingdate2.2(),Hurst[1],,AR(1),.2.2.1R/S2(a)2(b)R/S.2(a)n=310dR/S965:.310dH2=0.4543,,310d.n=310.Hurst0.66403,C=0.25532.2(b)[E(R/S)n](R/S)nV,.(R/S)nE[(R/S)n],E[(R/S)n],V310dVe(VeE[(R/S)n]V),310d.E(H)=0.57237,=4.7628,5%1.645,.2(a)R/S()Fig.2(a)R/Splot()ofdailyreturnsforShanghai2(b)R/S()Fig.2(b)R/Splot()ofdailyreturnsforShanghai2.2.2R/S,,3(a)3(b).n=60R/S,3(b)60(R/S)nE[(R/S)n],V60Ve,60(300d),.E(H)=0.60929,=1.7743,5%,C=0.2865.,,,Hurst,HurstHurst2.7%;,,Hurst.3(a)R/S()Fig.3(a)R/Splot()ofweeklyreturnsforShanghai3(b)R/S()Fig.3(b)R/Splot()ofweeklyreturnsforShanghai2.2.3R/SR/S4(a)(d),R/S450d90(Hurst0.451280.46246,),V450d90.Hurst0.636050.67699,3.45331.7758(5%).450d90.072004104(a)R/S()Fig.4(a)R/Splot()ofdailyreturnsforShenzhen4(b)R/S()Fig.4(b)R/Splot()ofdailyreturnsforShenzhen4(c)R/S()Fig.4(c)R/Splot()ofweeklyreturnsforShenzhen4(d)R/S()Fig.4(d)R/Splot()ofweeklyreturnsforShenzhen2.2.4R/S,R/S,5(a)5(b).,Hurst,,(R/S)nV,,IID,.,,R/S,IID,5(a)5(b)E[(R/S)n](4).R/S,R/S.5(a)R/SFig.5(a)R/Splot()ofdailyreturnswithdistortedsignsrandomlyforShanghai5(b)R/SFig.5(b)R/Splot()ofdailyreturnswithdistortedordersrandomlyforShanghai175:2.2.5R/S2.(2001),Hurst.,R/S,450d,(2002)215d.,,,R/S.2R/STable2R/Sresultcomparedwiththoseofotherscholars/dHurst/Hurst/dHurst/Hurst3100.664600.6824500.636900.677(1999)1950.661ªªª0.643ªª(2001)3160.68630.71ª0.67ª0.73(2002)1970.588400.6882150.617430.712(2002)3500.61ªªªªªª:ª;ª.2.32.3.1(volatility),,:annual=12month,EMH,.,,n,(n),6(a),.EMH,6(a)0.5.,n=300.45,300d.300d;300.Peters(1994)103(25000d)R/S,4.,,n300,,,310d.6(a)Fig.6(a)TermstructureofvolatilityofdailyreturnsforShanghai6(b)Fig.6(b)TermstructureofvolatilityofdailyreturnsforShenzhen272004102.3.2,6(b),420d,,420d(450d).2.4BDSBDSBrockDechertScheinkman[10],.ArvindMahajan[11]BDS10.BrockHsiehLeBaron[12]BDS(500).BDS,,,ADF-35.405-35.789(1%-2.566),,0.AICARIMA(p,0,q)(5)(6).xt=0.75575(8.9985)xt-1-0.69961(-7.6137)t-1+t(5)xt=0.87041(15.7809)xt-1-0.82438(-12.9980)t-1+t(6)t,BDS4.,BDS,,.4BDSTable4BDSstatisticsM23456789100.522.10929.15738.26649.19564.71488.137123.045177.170262.0541.021.66926.15929.57532.23035.32838.86442.81947.26952.6821.520.02623.69925.87426.88527.65428.57329.45830.30931.2972.017.43621.46922.97423.54123.70923.93524.14724.28824.4340.518.62626.03033.80942.81455.57674.892103.398150.370227.2431.019.02024.18928.18731.81935.75340.11945.03050.94658.2801.517.08220.89523.21425.02326.65128.09629.61431.18132.8632.015.07418.27319.69520.59421.29321.72422.07822.40822.744:M,,.5%1.645.3(1)Hurst0.5,,310d(60),450d(90).,,,(),,EMH,,,.,.(2)EMH,,.-..(3)R/S,,R/S.R/S.BDS.,.375::[1]PetersEE.FractalMarketAnalysisApplingChaosTheorytoInvestmentandEconomics[M].NewYork:JohnWilley&Sons,1994.[2]PetersEE.ChaosandOrderintheCapitalMarkets[M].NewYork:JohnWilley&Sons,1996.[3]OpongKK,MulhollandG,FoxAF,etal.ThebehaviourofsomeUKequityindices:AnapplicationofHurstandBDStests[J].JournalofEmpiricalFinance,1999,6:267282.[4],.R/S[J].,1999,(2):5962.XuLong-bing,LuRong.ExplorethenonlinearityinChinesestockmarketsbyR/Sanalysis[J].Forecasting,1999,(2):5962.(inChinese)[5],.R/S[J].,2001,(1):15.ZhangWei,HuangXing.EmpiricalstudyontheShanghaiStockExchangeandShenzhenStockExchangewithR/S[J].SystemEngineering,2001,(1):15.(inChinese)[6],.[J].,20