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1、TESTINGTHEMARKOVPROPERTYWITHULTRAHIGHFREQUENCYFINANCIALDATA∗JoaoAmarodeMatos˜MarceloFernandesFaculdadedeEconomiaGraduateSchoolofEconomicsUniversidadeNovadeLisboaFunda¸c˜aoGetulioVargasRuaMarquˆesdeFronteira,20PraiadeBotafogo,1901099-038Lisbon,Portugal22953-900RiodeJaneiro,BrazilTel:+351.21.382610
2、0Tel:+55.21.5595827Fax:+351.21.3873973Fax:+55.21.5538821amatos@fe.unl.ptmfernand@fgv.brMarch2001∗ThesecondauthorgratefullyacknowledgesthehospitalityoftheUniver-sidadeNovadeLisboa,wherepartofthispaperwaswritten,andaJeanMonnetfellowshipattheEuropeanUniversityInstitute.1TESTINGTHEMARKOVPROPERTYWITHU
3、LTRAHIGHFREQUENCYFINANCIALDATAAbstract:Thispaperdevelopsaframeworktotestwhetherdiscrete-valuedirregularly-spacedfinancialtransactionsdatafollowasubordinatedMarkovprocess.Forthatpurpose,weconsideraspecificoptionalsamplinginwhichacontinuous-timeMarkovprocessisobservedonlywhenitcrossessomediscreteleve
4、l.Thisframeworkisconvenientforitaccommodatesnotonlytheirregularspacingoftransactionsdata,butalsopricediscreteness.Further,itturnsoutthat,undersuchanobservationrule,thecurrentpricedurationisindependentofpreviouspricedurationsgiventhecurrentpricerealization.Asimplenonparametrictestthenfollowsbyexam
5、iningwhetherthisconditionalindependencepropertyholds.Finally,weinvestigatewhetherornotbid-askspreadsfollowMarkovprocessesusingtransactionsdatafromtheNewYorkStockExchange.ThemotivationliesonthefactthatasymmetricinformationmodelsofmarketmicrostructurespredictthattheMarkovpropertydoesnotholdforthebi
6、d-askspread.TheresultsaremixedinthesensethattheMarkovassumptionisrejectedforthreeoutofthefivestockswehaveanalyzed.JELClassification:C14,C52,G10,G19.Keywords:Bid-askspread,nonparametrictests,pricedurations,subordi-natedMarkovprocess,ultra-highfrequencydata.21.IntroductionDespitetheinnumerablestudie
7、sinfinancialeconomicsrootedintheMarkovproperty,thereareonlytwotestsavailableintheliteraturetochecksuchanassumption:A¨ıt-Sahalia(1997)andFernandesandFlˆores(1999).Tobuildanonparametrictestingprocedure,thefirstusesthefactt
