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1、epldraftEmergenceoflongmemoryinstockvolatilityfromamodifiedMike-FarmermodelGAO-FENGGU1,2,3andWEI-XINGZHOU1,2,3,4,5(a)1SchoolofBusiness,EastChinaUniversityofScienceandTechnology,Shanghai200237,China2SchoolofScience,EastChinaUniversityofScienceandTechnology,Shanghai200237,China3
2、ResearchCenterforEconophysics,EastChinaUniversityofScienceandTechnology,Shanghai200237,China4ResearchCenteronFictitiousEconomics&DataScience,ChineseAcademyofSciences,Beijing100080,China5EngineeringResearchCenterofProcessSystemsEngineering(MinistryofEducation),EastChinaUnivers
3、ityofScienceandTechnology,Shanghai200237,ChinaPACS89.65.Gh–Economics;econophysics,financialmarkets,businessandmanagementPACS89.75.Da–SystemsobeyingscalinglawsPACS05.40.-a–Fluctuationphenomena,randomprocesses,noise,andBrownianmotionAbstract.-TheMike-Farmer(MF)modelwasconstructe
4、dempiricallybasedonthecontinuousdoubleauc-tionmechanisminanorder-drivenmarket,whichcansuccessfullyreproducethecubiclawofreturnsandthediffusivebehaviorofstockpricesatthetransactionlevel.However,thevolatility(definedbyabsolutereturn)intheMFmodeldoesnotshowsoundlongmemory.Wepropo
5、seamodifiedversionoftheMFmodelbyincludinganewingredient,thatis,longmemoryintheaggressiveness(quantifiedbytherelativeprices)ofincomingorders,whichisanimportantstylizedfactidentifiedbyanalyzingtheorderflowsof23liquidChinesestocks.Longmemoryemergesinthevolatilitysynthesizedfromthemo
6、difiedMFmodelwiththeDFAscalingexponentcloseto0.76,andthecubiclawofreturnsandthediffusivebehaviorofpricesarealsoproducedatthesametime.Wealsofindthatthelongmemoryofordersignshasnoimpactonthelongmem-orypropertyofvolatility,andthememoryeffectoforderaggressivenesshaslittleimpactonth
7、ediffusivenessofstockprices.Introduction.–Thecontinuousdoubleauctionmecha-Inordertocheckifthemodelcapturessomebasicaspectsofnismisadoptedintheelectronictradingsystemsinmanystocktheunderlyingmechanismsgoverningtheevolutionofstockmarketsworldwide.Inparticular,mostemergingstockm
8、ar-prices,oneusuallyinvestigatesthestatisticalpropertiesofthearXiv:0
