经济系统分形机制与股票市场RS分析

200333:100026788(2003)0320009205RöS1,2(1.,100871;2.,100084):,,t,LEMH,RöSL,84.5LGZHL:;;RöS;H;:F830.91;O231.5:AMechanismofFractalinEconomicSystemandRöSAnalysisonStockMarketofChinaCAOHong2duo1,LIYing2(1.GuanghuaSchoolofManagement,PekingUniversity,Beijing100871,China;2.ElectronicalEngineeringDepartment,TsinghuaUniversity,Beijing100084,China)Abstract:Combiningstat2physicsoffbalancewiththefractaltheory,thephysicsmechanismwhyexistingfractalstructureisdiscussed.Afterwards,thedissipationpropertyofbehavioroffractaleconomictime2seriesisdiscussed,andtheevolvementofK2entropyisexplained.ShenzenstockmarketisresearcheddependingonRöSanalysisandconclusions,whichhavebeenobtainedabove.ItindicatestherearealongperiodandashortperiodinShenzenstockmarket,andtheyleaveeachothertobe4.5yearsand8months.ThemechanismwhydifferentHindexiscreatedfromdifferenttimeseriesinthesamesystemismadeclear.Keywords:economysystem;fractaltime2series;RöSanalysis;Hindex;dissipationcharacter:2001208202:(79970043):,(1972-),,,,,1,;,,L,L,,,L,(FBM),,LF2Px(t)P(x,t)[1,2]:Pt=DPxx(1)D,,Z©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.t=0x(0)=0,Langevinmx+axa=F(t)(2)m,,;a,;F(t),ZBM,,,F(t)Z,F(t)=0,F(t)F(0)F(t)=AD(t-0),AZ,F(t)=0,F(0)F(t)=a02Ht-2H(3),(1)Pt=Dõ2Hõt2H-1PXX(4)FBMZ(4)P(x,t)=14PDt2Hexp-x24Dt2H(5)(5)FBM,HHurstZx(t)=0(6a)x2(t)=2Dt2Ht2H(6b),P(x,t):Px=bHx,t=bH2,t=b-HP(x,t)(7)(4)D=2DHt2H-1D,t1,H12;t1,H12=D,H=12D,t1,H12;t1,H12(8)t,Smin,(8)SminK2ZDD:,;0,Z(8)ZLagevinF(t)(3),x2(t),Z,F(t)D,;t,ZZ(7)FBM,P(x=bsx,t=bqt)=KrP(x,t)(9),S=H,q=1,r=-HZ:x=bsxt=bqx(10)(9),0120033©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Pt=bq-rPtPxx=b2s-rPxx(11)(11)(4)Pt=Db2H-1Pxx(12)D{=Dõb2H-1D,b1,H12=D,H=12D,b1,H12(13)(13)FBMLFBMZ,,Z2RöS(EMH)L,L,,,L,L,,L,L,EMH,,L,,L,(CapitalAssetPrecingModel,CAPM)(ArbitragePricingTheory,APT),L,EMH:1.,,L;,,,L2.,L,L,;,,L,,L3.,LH=12EMHFMHLFMHL,MandelbrotBB[3]:R(h)öS(h)=(ah)Ha,hLH(HEHurst)RöS[3]L{F(t)},t=1,2,h1:113RöS©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Nh=1h6ht=1N(t),h=1,2,x(t):x(t,h)=6hu=1(N(u)-Nh),1thR(h):R(h)=max1FtFhx(t,h)-min1FtFhx(t,h),h=1,2,S(h):S(h)=1h6hi=1(N(t)-Nh)212,h=1,2,R(h)öS(h),h=2,3,lnRöS-lnh,HZRöS(1991.4.3-1999.12.15)ZGZ$t=1,GZ$t=5,GZ$t=10,GZ$t=20,Z11Z1GZHNTsTlHTsrTsHTsGZ$t=1200016010800.93080.95030.0286GZ$t=5400322160.91090.95020.1593GZ$t=10200161080.86220.99210.0674GZ$t=201008540.87330.99810.04561GZHHT1rT1HT1HrHHH0.70780.87540.01730.65070.93620.02050.78230.89850.07050.70000.94740.08450.87110.92460.08210.69060.94340.10240.88870.94660.08950.75760.96150.1042:1.1,H12,ZZ2.1,RöSZT=160,T=1080,ZT1080,H12ZZZGZ$t=1H$t=1=0.65,Ts=160(TS)Z3.11,1080544.5Z,ZZ,H12,Z,ZH12,:Z,Z,,Z,54,4.5,ZZ4.GZ($t=1,$t=5,$t=20)H,HSHZZGZ2120033©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.$tH,Z(3):,HZ,,Z(a)GZ$t=1(b)GZ$t=5(c)GZ$t=10(d)GZ$t=201RöS3,,,K2LEMH,RöSL,84.5,1997,20016L,GZHL:.:[1]R.Balecu.[M]..:,1989.68-193.[2].[M].:,1988.353-425.[3]MandelbrotBB,VanNessJW.FractionalBrownianmotion,fractionalnoiseandapplication[J].SIAMRev,1968,(10):422-437.[4][].[M].,.:,1996.318-319.[5]MandelbrotBB.TheFractalGeometryofNatures[M].SanFrancisco:W.H.FreemanangCo,1982.96-105.[6].[D].:,2000.313RöS©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.