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6LongMemoryandCrudeOil'sPricePredictability
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10RoyCerqueti&VivianaFanelli
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131DepartmentofEconomicsandLaw,UniversityofMacerata,
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16ViaCrescimbeni,-62100Macerata,Italy.
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18Email:roy.******@
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21DepartmentofEconomics,ManagementandBusinessLaw,UniversityofBari
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23LargoAbbaziaSantaScolastica53,70124Bari,Italy.
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25Email:viviana.******@
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31Abstract
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34Thispaperdiscussestheusefulnessofthelongtermmemorypropertyinpricepre-
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,theHurst'sexponentsrelatedtoawidesetofportfoliosgenerated
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38bythreecrudeoilsareestimatedbyusingthedetrended
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40aim,thedailyempiricaldataonWestTexasIntermediate,BrentcrudeoilandDubai
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44speci ccombinationsareassociatedtopersistence/antipersistencelong-runbehaviors,
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showsthatlongtermmemorycane ectivelyserveaspricepredictor.
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52Keywords:Commoditiesportfolio,Hurst'sexponent,Statisticalarbitrage,Pricepredictabil-
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54ity.
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56Correspondingauthor.
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1Introduction
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3Agreatstrandofliteratureontimeseriesdealswiththeanalysisoftheso-calledpersis-
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5
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8accuratestudyofthelong-
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11formalizationoftheconceptoflongtermmemorypropertywasde nedbyHurst(1951)for
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13thespeci
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15Nile
owfortheprojectofariverdam,andidenti edaparameterH2(0;1)(theso-called
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18Hurst'sexponent)associatedtotherateofdecayoftheautocorrelationasafunctionofthe
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20autocorrelationlag.
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22IfH=0:5,thecurrentvalueoftheserieswouldnotdependentofpastvaluesofthese-
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25ries,
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27[0;0:5],theseriesbecomesanti--persistentseriesdescribe`mean-reverting'
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ctimeinterval,itislikelyto
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32reduceinthefollowingone,
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34revertingbehaviorincreasesasHurst'
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37Hexponentvariesbetween0:5and1,theseriesispersistent,whichmeansthatitistrend
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.
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42Amongothers,CorazzaandMalliaris(2002),CajueiroandTabak(2004),Kyawetal.
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44(2006),SinghandPrabakaran(2008),Kloedenetal.(2011),Giles(2008)andPotgieter
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46(2009)showthattheanalysisofthemainfeaturesofthetimeseriesprovidessomekey
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48
(1996)suggeststhattheexis-
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51tenceofalongtermmemoryassociatedwithslowdecayofautocorrelationfunctionsinasset
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54returnsindicatestheexistenceofexploitablemarketine.(2018)pro-
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56poseanovelagent-
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592
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theHurst'.(2015)focusonmul-
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2tifractaltheoryforinvestigatingstatisticalpropertiesofenormousandirregulardatasets.
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5Multifractalstructurediagnosis,tendencyandsingularityanalysisareappliedtooilprices
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.(2018)use
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10theHurst'sexponenttoexplorethelongtermmemorypropertyofthevolatilityofanew
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ndsomelong-runpathsandregularitiesin
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14theindexriskiness.
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17Inthewidespectrumofinformationbroughtbytheassessmentofthelongtermmemory
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19property,itisworthytomentionthepresenceoftheso-calledstatisticalarbitrage(StatArb,
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hereafter).TheStatArbcouldbedescribedastheattempttopro tfrompricingine-
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24cienciesidenti (2000)andBondarenko
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26(2003)aStatArbisageneralizationofthetraditionalzero-
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29lattercase,-pricerelationshipsbetween
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31assetpairswithidenticalcash-
owsareconstructedandpurearbitrageopportunitiesare
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identi .(2005)astatis-
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36ticalarbitrageisalonghorizontradingopportunitythatgeneratesrisklesspro
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38naturalextensionofthetradingstrategiesutilizedintheexistingempiricalliteratureon
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nedwithoutanyreferencetoanyequilibriummodel,therefore,its
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43existenceisinconsistentwithmarketequilibriumand,byinference,markete
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45couldsaythatStatArbenablestherejectionofmarketeciencywithoutinvokingthejoint
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48hypothesisofanequilibriummodelandreplacingitwithanassumedstochasticprocessfor
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50tradingpro ,seealsoBurgess(1999),Elliottetal.(2005),Do
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53etal.(2006),Bertram(2010),AvellanedaandLee(2010).ThetermStatArbwasusedfor
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55the rsttimeinthe1990sandremainedwidelyusedbyoperatorsin nancialmarketsuntil
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,by2000dramaticchangesinmarketdynamicsledtoweakperformance
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2ofexistingmodelsand,consequently,StatArbsstartedtocommandlessattentioninthe
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(2007),renewedinterestforthemreturnedonlyin2006,when
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7moreaccuratealgorithmssecuredbetterresults.
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10WerefertoStatArbasazero-costtradingstrategyforwhichtheexpectedpayo ispositive,
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12andtheconditionalexpectedpayo ineach nalstateoftheeconomyisnonnegative,ina
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14 nite-horizoneconomy.
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17ThepersistencepropertiesofatimeseriesandStatArbarelinkedthroughtheconceptsof
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19strongstationarityandcointegration(EngleandGranger(1987)).Infact,itisimportantto
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stressthatthecointegrationofthepricesleadingtoa(strongly)stationaryprocessidenti es
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24thepresenceofstatisticalarbitrageforsomeportfoliosgeneratedbytheassetsthemselves.
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29propertiesasdescribingthestrongstationarityofthepriceofaportfolio{henceleadingto
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31StatArb{,somewordscanbeprop-
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38authorsas,forexample,Ortiz-Cruzetal.(2012)andKristoufekandVosvrda(2014)),in-
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41vestigatetheeciencyofcrudeoilmarkets,andmanyothersanalyzelong-rundependence
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-Ramirezetal.(2002)andSerletisand
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45Andreadis(2004)thatstudythelong-runmemorymechanismthata ectsthecrudeoil
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48priceevolution,andTabakandCajueiro(2007)thatshowthetemporalmovementofthe
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50crudeoilmarkettowardse-Ramirezetal.(2008)empirically ndevidences
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53oflong-runautocorrelationsincrudeoilmarketstowardsecienciesandtheyanalyzealso
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55short-termautocorrelationsonthebasisoftheestimationoftheHurst'sexponentdynamics.
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Theauthorsemploythedetrended
uctuationanalysisasstatisticalmethodologicaltool.
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2WangandLiu(2010)extendtheexistingliteraturebytestingfortheeciencyofWTI
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5crudeoilmarketthroughobservingthedynamicoflocalHurst'
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7themethodofrollingwindowbasedonmultiscaledetrended
uctuationanalysis,and nd
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10thatlarge
uctuationsofWTIcrudeoilmarkethavehighinstability,bothintheshort-and
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12longterms,whilesmall
(2018)discussthelong
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14termmemorypropertyoftheoil-gaspricerelationshipinordertoclarifywheneversucha
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17linkisofpermanenttypeoroftransitorynature.
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cally,weconsideroneofthetypical
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examplesoflong-runrelationsoncommoditymarkets:therelationamongthreecrudeoils,
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24quotedindi erentmarkets,WTI,,itisnaturalthinkingthat
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26threeassets,havingsamespeci cfeaturesandsupplyanddemandwiththesamecharac-
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29teristics,havepricesthatarein
uencedbymarketrumorswiththesamemagnitudeand
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31incrementaldirection.
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Inordertofacetheproblem,weproposeastatistical-basedanalysisoftheempiricalport-
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36foliosobtainedbytheavailablecommoditiesdata,anddiscussthelong-runpropertiesof
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38themthroughtheestimationoftheHurst'sexponentH.
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41ThereisawidesetofquantitativetoolsforestimatingthevalueofH(
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43etal.(2011)).Amongthem,themostprominentoneisthealreadymentionedDetrended
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45FluctuationAnalysis(DFAhereafter,Pengetal.(1994)).Indeed,thisprocedureovercomes
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48someshortcomingsoftherescaledrangeR=SprocedureofHurst(1951).Thisexplainsthe
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50popularityoftheDFAforestimatingHandalsoourchoicetoemployDFAfordeveloping
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,werefertheinterested
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55readertoPengetal.(1995);Hardstoneetal.(2012);HeandChen(2011).
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OurpaperisclosetoCerquetietal.(2018),whichdealswiththelongmemoryofcrudeoil
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2portfolios,,thequotedpaper
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5considersonlyascenarioanalysisonafewcasesofportfolios{elevenofthem,tobeprecise
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7{andmakesinferenceonthestatisticalhypothesisthattheirpriceshaveHurst'sexponent
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10H=0orH=0:
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12derivetheHurst'
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14Hurst'sexponentsdistributions,tohavemoreinsightsonthedynamicsofthemispricing
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,wearealsoabletoexploretherelationshipsbetweentheHurst's
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19exponentsandthesharesofcapitalinvolvedintheconsideredcrudeoils,henceanswering
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tothekeyquestiononhowthedi erentcapitalallocationrulesa ectthelongmemory
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{anddi erentlywithCerquetietal.
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26(2018){wearehereabletodiscussalsosomestylizedfactsincommodity nanceontheba-
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29sisoftheparamountviewoftheHurst',someinterestingresults
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31havebeenhereobtained: rst,awidepartofmispricingportfoliosexhibitsanantipersistent
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long-runbehavior,withHurst'sexponentH<0:5;second,wehaveshowntheexistenceof
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36someportfoliosfollowingageometricBrownianmotion,whichisstronglyconnectedtothe
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38presenceofstatisticalarbitrageopportunities;third,theHurst'sexponentsoftheportfolios
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41varywithanunexpectedregularityasthequotesofportfoliochange;fourth,innocasesone
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43canobservenoteworthylong-runpersistenceoftherelatedportfolios,hencecon rmingthe
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45mean-revertingnatureofthecommoditiesportfoliosprices; fth,thesimulatedtrajectories
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48whenH=0:
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50 ndingisofparticularinterest,sinceitstatesthattheestimationoftheHurst'sexponent
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53mightleadtoanexcellentdeviceforpricepredictability.
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55Therestofthepaperisorganizedasfollows:Section2containstheformalizationofthe
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model;Section3isdevotedtothedescriptionofthedataandoftheemployedmethodol-
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2ogy;Section4describesanddiscussestheoutcomesoftheanalysis;lastSectiono erssome
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5conclusiveremarks.
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Long memory and crude oil’s price predictability 2019 Roy Cerqueti 来自淘豆网www.taodocs.com转载请标明出处.