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on hurst exponent estimation under heavy-tailed distributions

on hurst exponent estimation under heavy-tailed distributions

ID：7348915

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页数：20页

时间：2018-02-12

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1、OnHurstexponentestimationunderheavy-taileddistributionsJozefBarunikLadislavKristoufekyAbstractInthispaper,weshowhowthesamplingpropertiesofHurstexponentmethodsofestimationchangewiththepresenceofheavytails.WerunextensiveMonteCarlosimulationsto ndouthowrescaledrangeanal-ysis(R=S

2、),multifractaldetrended uctuationanalysis(MFDFA),detrendingmovingaverage(DMA)andgeneralizedHurstexponentap-proach(GHE)estimateHurstexponentonindependentserieswithdif-ferentheavytails.Forthispurpose,wegenerateindependentrandomseriesfromstabledistributionwithstabilityexponentch

3、angingfrom1.1(heaviesttails)to2(Gaussiannormaldistribution)andweestimateHurstexponentusingthedi erentmethods.R=SandGHEprovetoberobusttoheavytailsintheunderlyingprocess.GHEprovidesthelow-estvarianceandbiasincomparisontotheothermethodsregardlessthepresenceofheavytailsindataandsa

4、mplesize.Utilizingthisresult,weapplyanovelapproachofintradaytime-dependentHurstexponentandweestimateHurstexponentonhighfrequencydataforeachtradingdayseparately.WeobtainHurstexponentsforS&P500indexfortheperiodbeginningwithyear1983andendingbyNovember2009andwediscusssurprisingres

5、ultwhichuncovershowthemarket'sbehaviorchangedoverthislongperiod.Keywords:Hurstexponent,heavytails,highfrequencydataanalysisarXiv:1201.4786v1[q-fin.ST]23Jan2012InstituteofInformationTheoryandAutomation,AcademyofSciencesoftheCzechRe-public,InstituteofEconomicStudies,CharlesUniv

6、ersity,Prague,Email:barunik@utia.cas.cz(CorrespondingAuthor)yInstituteofInformationTheoryandAutomation,AcademyofSciencesoftheCzechRe-public,InstituteofEconomicStudies,CharlesUniversity,Prague11IntroductionThepresenceoflong-rangedependenceandtheestimationofitscharacteristicHurs

7、texponentin nancialtimeserieshavebeenwidelydiscussedinseveralrecentresearchpapers,e.g.(Alvarez-Ramirezetal.,2008;Carboneetal.,2004;Czarneckietal.,2008;DiMatteo,2007;DiMatteoetal.,2005;GrechandMazur,2004;Matosetal.,2008;Peters,1994;Vandewalleetal.,1997).Eventhoughtherearesevera

8、lstudiesofthe nitesamplepropertiesofdi erentmeth-ods(Couillar

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