加权股票网络中的无标度行为研究

:[e-mail]dstocknetwork(WSN)modelofstockmarketispresentedbasedonthecomplexnetworktheory.Inthismodel,eachvertexofthenetworkdenotesastock,andtheweightassignedtoeachedgeisthecross-correlationcoefficientsofreturns.Wedefinethepositive(ornegative)influence-strengthofastockasitscapabilitytocauseotherstocks’pricetorise(orfall)whenitspricerises.Thenwefindthattheinfluence-strengthdistributionfollowsapower-lawwithexponentr=1.77.Theresultshowsthattheremustbeafewstockswhosepricefluctuationscanpowerfullyinfluencethepricedynamicsofotherstocksinthesamemarket.Furthereconometricanalysisrevealstherearesignificantdifferencesbetweenthepositiveandthenegativeinfluence-strengthsinmostofyears.KeywordsStocknetwork,Power-law,Jarque-Beratest,Kruskal-Wallistest1IntroductionGenerally,socialandeconomicsystemsalwaysconsistofmanyconstituentssuchasindividuals,companiesandcountries,etc.,exhibitingcooperativeandadaptivephenomenathroughvariousinteractionsbetweenthem.Itisexactlytheseinteractiveandadaptivebehaviorsthatmakesthecomplexsocialandeconomicsystemspresentaseriesofmacroscopicbehaviorsandpatterns,suchascommodityprices,stockpricesandexchangerates,etc..Inordertoexplainthesephenomenainsocialandeconomicsystems,researchersfirstlyresortedtoErdos-Renyi(ER)modelofRandomGraphTheory(RGT).ButERmodeldidnotexplainthescale-free(SF)behaviorcommoninrealworld.In1999,amodelofnetworkgrowthwasfirstputforwardbyA.-L.BarabasiandR.Albertbasedonpreferentialattachment,thatwasBarabasi-Albert(BA)model[1].ItiswellknownthattheBAmodelexplainsthescale-freebehaviorincomplexrealworldverywell.WeshouldpointoutthattheERmodelandtheBAmodelareallBinaryRandomGraph(BRG)models.Andinthesemodels,theweightassignedtoeachedgeis1or0,indicatingtheexistenceornotoftheedge.Butitistoosimplifiedtosettheweightas1or0.Inreality,theweightsusuallyrangefrom–1to1,thatisWeightedRandomGraph(WRG).In2001,S.H.Yook,H.JeongandA.-L.BarabasihavestudiedtheWRGtheoretically[2].Andtheyalsofoundthescale-freebehaviorintheirmodelconditionally.Inthesameyear,H.J.KimandY.Lee[4]haveresearchedthestockpricebehaviorsbetweentheS&P500companiesbasedonWRG,whereallvertices(companies)arefullyconnected.Intheirresearch,theyfoundthepower-lawdistributionwithexponentbelow2,whichis3inBAmodel[3].Inthispaper,wehavestudiedtheShanghaiA-sharemarketbasedonWRG.Wedefinedthepositiveandthenegativeinfluence-strength(IS)toanalysisthedifferenceoftheinfluencecapabilitiesandformsbetweenstockpricefluctuations.Ourresearchshowsthattheinfluence-strengthfollowsapower-lawdistributionwithexponent1.77.Andfurthereconometricanalysisrevealstherearesignificantdifferencesbetweenthepositiveandthenegativeinfluence-strengthsinmostofyears.1SupportbySpecializedResearchFundfortheDoctoralProgramofHigherEducation(20020248020).(WSN)modelshowninfigure1.Inthismodel,eachvertexofnetworkdenotesastock,andeachedgeisusedtodescribetheinfluencerelationshipbetweenstockpricefluctuations.Theweightassignedtoeachedgeisthecross-correlationcoefficientsofreturns.VertexEdgejiw,Figure1.TheWeightedStockNetworkThroughusingoftheRandomMatrixTheory(RMT)[6]andeconometricanalysis,wehavestudiedtheinfluencerelationshipbetweenstockpricefluctuationsofdifferentcompaniesinthesamemarket,andrevealedsomedisciplinesimpliedinit.3DistributionoftheCross-CorrelationCoefficientsofReturns3.1Definitionofthecross-correlationcoefficientsofreturnsBasedontheweightedstocknetworkmodelpresentedabove,wewillconductanempiricalanalysisinthefollowingcontext.Oursamplespacesofresearchare550stocksofShanghaiStockExchange(SSE),fromJan.4,1999toDec.31,2002,whichareprovidedbytheResearchCenterforModernFinanceofShanghaiJiaoTongUniversity.Letbethestock-priceofacompanyiattime.Thenthereturnofthestock-priceafteratimeintervalisdefinedas)(tXitt∆Y)(ln)(ln)(ttXtXtiii∆−−=(1)whereday,i.Inordertoavoidthetime-dependentbehaviorofthemeanvaluemightbecausedbyexternaleconomicenvironmentssuchasbankinterest,inflationindex,exchangerate,etc.,whichfluctuatesfromtimetotime,Weintroduceaquantity,1=∆tN,,1L=∑−=iiiitYNtYt)(1)()(C(2)whereCmeanstherelativereturnofacompanytoitsmeanvalueovertheall550companiesattimet.Thenwecandefinethecross-correlationcoefficientsofreturnsas)(tii))((2222,−−−=jjiijijijiCCCCCCCCw(3)wherethebracketsmeanatemporalaverageovertheperiodwestudied.Thecross-correlationcoefficientistheweightassignedtotheedgeconnectingbetweenverticesiandjiw,j,andvariesfrom–1to1.