中国国债收益率的多标度分析

1117Matlab~0.0595δ17010103009908010107CopheneticC93A1homogeneous[1][2][3][4][5][6][7]17047105121979.8,Email:[e-mail]022278902459041300072()ln()ln(1)iiirtptpt=−−1()irtit()ipt(1)ipt−it1t−117ij,1,...17ij=111222211111()()()()11[()(())][()(())]TTTijiitttijTTTTiijjttttrtrtrtrtTCrtrtrtrtTT=======−=−−∑∑∑∑∑∑∑2T()(1,2,17)irti=LTRMantegna[8]ijC(,)2(1)ijdijC=−33(,)0dijij=⇔=(,)(,)dijdji=(,)(,)(,)dijdikdkj≤+(,)dij[0,2](1,2,...17)ii=TRt11()()TiitirtrtTσ=−∑iσiijCijcosijijCθ=1i=1j=ijijijTR,cosijijijijθ==ijTRijC,ijijC=(,),,,,,2(1)ijdijijijijiiijjijjC=−=−−=−−+=−2,1(1,2,...17)iiii===617δiδδδ0δ=2δ=δ17Matlab6.5linkageUhierarchicaltree141317931210172561181415160.050.10.150.20.250.30.35Biδ117Fig.1.Theclusteringstructureofshanghaistockexchange’s17treasurybonds1Uδ~0.0595δ171117Table1.Theclusteringresultofshanghaistockexchange’s17treasurybonds000696009704010004010010010103009905009908010110010112010203010210010301010107010213010115010214010215Cophenetic0.9710173Mandelbrot[10]1963()rtMassimoetal[11]1()(,)()ln()tptrtrttptτττ′=+′=+=∑55τ1,2,...20τ=5(,)rtτ[12]()(,)ln()ln()qqqttSrtptptτττ==+−6⋅t[13]()~hqqSττ−h0.5h=6Roberto[14]()()~qqSθττ−7()qθ7ln()()lnqSqταθτ=−88q()qθ1,2,...10q=matlab1()qθ110101030099080101070102130101150102151()qθ2()qθ3()qθ4()qθ5()qθ6()qθ22q()qθTable2.Themulti-scalingfunction()qθgiventhevalueofqq123456789101()qθ0.99250.9929099210.99220.99210.99220.99210.99220.99210.99222()qθ0.99270.99310.99230.99230.99220.99220.99220.99220.99220.99223()qθ0.99260.99230.99210.99220.99210.99210.99210.99210.99210.99214()qθ0.99230.99230.99220.99220.99210.99210.99210.99210.99210.99215()qθ0.99220.99220.99210.99210.99210.99210.99210.99210.99210.99216()qθ0.99210.99210.99210.99210.99210.99210.99210.99210.99210.99212010103009908010107θ(q)qθ(q)θ1(q)θ2(q)θ3(q)θ4(q)θ5(q)θ6(q)2q()qθFig.2.Differentvalueofqandthemulti-scalingfunction()qθofsixtreasurybonds2ARCH4δ~0.0137δ17010103009908010107[1]SV[J]20011119610821-26BaiKun,ZhangShiying,ExtendedsvmodelandItsapplicationinShenzhenStockMarket[J],SystemsEngineering,Nov.,2001,Vol.No.6,21-26.[2]AR-X-GARCH[J]20026273303-308PengZuoxiang,PangHao,HypothesisoffinancialmarketefficiencywithapplicationsofAR-X-GARCHmodels[J],JournalofSouthwestChinaNormalUniversity(NaturalScience),Jun.2002,Vol.27,No.3,303-308.[3][J]2003812485-90WangWeining,WangBinghong,ChenYi,ThestatisticanalysisoftheindexofShanghaiSecurities[J],OperationsResearchandManagementScience,Aug.,2003,Vol.12,No.4,85-90[4][J]20046193294-299ZhangYongdong,Temporaldimensionofrisk:empiricalinvestigationofChina’sstockmarket[J],JournalofSystemsEngineering,Jun,2004,Vol.19,No.3,294-299.[5]DidierSornette,AndersJohansen,Ahierarchicalmodeloffinancialcrashes[J],PhysicaA261(1998),581-598.[6]R.N.Mantegna,Informationandhierarchicalstructureinfinancialmarkets[J],ComputerPhysicsCommunications121-122(1999),153-156.[7]L.Marangio,A.Ramponi,M.Bernaschi,Acriticalreviewoftechniquesfortermstructureanalysis[J],Int.J.Theor.Appl.Finance5(2002),189-221.[8]R.Mantegna,H.E.Stanley,Scalingbehaviorinthedynamicsofaneconomicsindex[J],Nature376(1995),46-49.[9]LucaGrilli,Long-termfixedincomemarketstructure[J],PhysicsA332(2004),441-447.[10]B.B.Mandelbrot,Thevariationofcertainspeculativeprices[J],J.Business36(1963),[11]MassimoBernaschi,LucaGrilli,DavideVergni,Statisticalanalysisoffixedincome[J],PhysicsA308(2002),381-390.[12]J.P.Bouchaud,M.Potters,M.Meyer,Apparentmultifractalityinfinancialtimeseries[J],Eur.Phys.J.B13(2000),595-599.[13]B.V.Gnedenko,A.N.Kolmogorov,Limitdistributionsforsumsofindependentrandomvariables[J],Reading,MA,1954.[14]RobertoBaviera,MichelePasquinietal,Effciencyinforeignexchangemarkets[EB/OL].’rangeofvolatilityofTreasurybonds010103,009908and010107arelargeandshowstheevidentnon-linearcharacter,whilethescalingfunctions’rangeofvol