非线性动力学分析在股票市场中应用

:100629798(2001)0420005207,(,266071):,,,,:;;:N941.4:A,,,,,,,,,,ARMA,,,,,,11.1,,EMH,,,,,,,,,nx1,x2,,xn,t,xi=xi(t),dx1dt=f1(,x1,x2,,xn)dx2dt=f2(,x1,x2,,xn)dxndt=fn(,x1,x2,,xn)(1),fixi164200112JOURNALOFQINGDAOUNIVERSITYVol.16No.4Dec.2001:,(19662),,,,:,:79970114:2001209210©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,nn,n,t,,,,,,,,,,,,,,,,,,,Grassberger-Procaccia,,,,1.21)Nx1,x2,x3,xi,,xN(2)m,,x1,,m,mr1r1:(x1,x1+,x1+2,,x1+(m-1))(3)2)x1,x2,r2:(x2,x2+,x2+2,,x2+(m-1))(4)3)NNm=N-(m-1),mr3:(x3,x3+,,x3+(m-1))r4:(x4,x4+,,x4+(m-1))rN-(m-1):(xN-(m-1),xN)(5),m,Nm2,,,1996,19961022200102281050,Di(1),,matlabsspsvb1(199610222001228)2,,,xi(2)xi=ln(Di)-(bi+b0)(6)xi,Di:b,b0616©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Di,i2,xi,,,,xi(34)34,,,,,2.1,,,HurstR/S(rescaledrangeanalysis),,,xi,AN,,X(a,t)=ti=1(XN3(a-1)+i-Ma)t=1,2,,N(7),X(a,t)a,XN3(a-1)+iai,Maa,N,NRR=max(X(a,t)-min(X(a,t))(8),,,R/S=(bN)H(9)R/S,N,b,H,0H1R/S,AR/S,AR/S,NR/S,N,R/S,log(R/S)-log(N),log(R/S)log(N)HH=0.5,,,,H0.5,,,log(R/S)log(N),,N,H,H,,,,H,,H[1]5log(R/S)-N,log(R/S)N74,:©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.N,,5,120,120,120(N120)log(R/S)-log(N),H0.700.51(0.9910.967),,,,,,1205R/S:log(R/S)2N2.2,,,,,,Haus2dorff,,,,,d(ri,rj)=[m-1k=0(xi+k-xj+k)1/2](10)r,d(ri,rj)r,rNm(Nm-1)C(r),C(r)=1Nm(Nm-1)i,Nmj=1,ij(r-d(ri,rj)(11)(x),(x)=1,x00,x0(12)r,C(r)rC(r)=rD(13),D,D=limr0lnC(r)/lnr(14),r,C(r),lnC(r)lnrD,m,Dm,D678,,,,,,,816©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,,6,5,,,5,,Wolf,,,[1],120,5,24,6,20,Xi,77,1.6-2.6,,(8)8,,,,,1,,2.3,,:,,,,,,,[2],,,,,,,,0[3],,,9Xi,,,0,,,,1199781519982191.652.0219971231998631122.541420.00199822019983312.021.8019986419988181413.081420.0019984119984231.80199881919995181059.871071.301998424199811191.802.42199951919996291109.081739.20199811201999982.422.271999630199912271689.421345.351999992000832.272.501999122820008211348.822108.6920008420012282.512.572000822-1875.912124.6194,:©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,,,,,;,,,9[4](1)(2)x0,x0,V0,,L0(3)0,V0V1,x(t0+0)y(t0+0),L1,0L0L1,1,L1=L0e10(15)1=10log(L1/L0)(16)(4)x(t0+0),V1,,V1,V1,2,2=11log(L2/L1)(17),k,=1NkNkk=11Tk-1ln(Lk/Lk-1)(18)(5)m,,m,,,,,,,,Wolf,10%[1],8155,(10)1010,,0.0073/,(1),,,,,,,(2),0.0073/,0.0073/,0116©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,1/0.0073(136),,,136R/S1203,(1),1.62.6,,23(2)R/S,,0,(3),,,120,120,(4),H,,,,:[1]PetersEE.Chaosandorderinthecapitalmarket[M].secondedition.NewYork,1991.[2].[M].:,1995.[3]H,.()[M].:,1992.[4],.-[M].:,1995.NONLINEARDYNAMICSANALYSISONSTOCKMARKET-INCASEOFSHANGHAISTOCKMARKETWuHaihua,Lidaoye(CollegeofFinancialScience,QingdaoUniversity,Qingdao266071China)Abstract:Transcendingthelinearmodeltraditionaleconomicsresearchandregardingsecuritiesmarketasanon2linearsystem,aempiricalanalysistothekineticpropertyofShanghaisecuritiesmarketwasgivenbysomecom2plexitytheoretics,suchasfractalandchaostheories.Thefractalcharacteristics,theextentofcomplexity,thestyleofmovementandthestabilityofShanghaisecuritiesmarketaregotlen,andtherearedistinctivefractalstru2turesinShanghaisecuritiesmarket.Thetheoreticalsignificancesandpracticalrelevanceofthisconclusionsareal2sodiscussed.Keywords:stockmarket;system;dynamicsanalysis114,:©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.