ForecastingFinancialTimeSerieswithSupportVectorMachinesBasedonDynamicKernels
JohannesMager
InstituteofComputerArchitecturesUniversityofPassau,GermanyEmail:mager@ m.uni-passau.de
UlrichPaasche
NeuralResearchCenterMunichGmbH
Munich,Germany
Email:ulrich.paasche@nrcm.de
BernhardSick
InstituteofComputerArchitecturesUniversityofPassau,GermanyEmail:sick@ m.uni-passau.de
Abstract—Thetechnicalanalysisof nancialtimeseriesandinparticularthepredictionoffuturedevelopmentsisachallengingproblemthathasbeenaddressedbymanyresearchersandpractitionersduetothepossiblepro t.Weprovideaforecastingtechniquebasedonacertainmachinelearningparadigm,namelysupportvectormachines(SVM).SVMgainedmoreandmoreimportanceforpracticalapplicationsinthepastyearsastheyhaveexcellentgeneralizationabilitiesduetotheprincipleofstructuralriskminimization.However,standardkernelfunctionsforSVMarenotabletocomparetimeseriesofvariablelengthappropriately,i.e.,whenweassumethatthesetimeseriesmustbescaledinanon-linearway.Therefore,weusethedynamictimewarping(DTW)techniqueasakernelfunction.Wedemonstratefortwo nancialtimeseries(FDAXandFGBLfutures)thatexcellentresultscanbeobtainedwiththisapproach.
I.INTRODUCTION
Thepredictionoffuturestockmarketdevelopmentsisaproblemthathasbeenattractingtheattentionofbothpracti-tionersandresearchersformanydecades.Itcaneasilybeseenthattherearecertainrecurringpatternsinthehistoryofmarketprices,andtherearevariousapproachesforclassifyingthem[1],[2].Butamuchhardertaskistorecognizesuchpatternsintheconstantlyevolving nancialmarketsearlyandwithsuf cientreliability.Evenworse:Itstillisheavilydisputed,whetherchartpatternsallowforapredictionofcertainfutureeventsatall.
Inthisarticle,weproposeamachinelearningtechniqueforforecasting nancialtimeseries,whichreliesonthepopulartechniqueofsupportvectormachines(SVM).Usingalargehistoricalsetofreal-world nancialtimeseries,weexaminetheperformanceofdifferentvariantsandparametersettings.Tofurtherincreasethepredictionaccuracyontimeseries,standardkernelsoftheSVMarereplacedbyspecialdynamickernelfunctions,whichareadaptedforanalyzingtemporaldata.Wewillshowthattheutilizationofthesekernelsresultsinasigni cantlybetteraccuracyanditbecomespossibletooutperformthemarket’soveralldevelopment.
Withtheintegrationofthistechniqueintoaframeworkfortechnicalanalysis,Investox,itisalsopossibletoevaluatetheperformanceusingavirtualtradingagentonhistoricaldataandusethesystemon“live”datafeeds.
Thearticleisorganizedasfollows:InSectionII,weprovideashortinsightintotheprinciplesoftechnicalanalysisand nancialmarketdataanddiscusssomerelatedwork.In
SectionIII,SVManddynamickernelfunctionsareintroduced.SectionIVfollowswiththeexperiments:We rstexplaintherationalebehindtheconstructeddatasetsandsetouttheutilizederrormeasures.Thereafter,theresultsofourexperimentsaredocumented.Finally,SectionVsummarizesthemajorinsightandgivesanoutlooktofutureresearch.
II.FINANCIALANALYSIS
A.PrinciplesofTechnicalAnalysis
Theanalysisof nancialmarketscanbedividedintotwobig elds:Whereasfundamentalanalysistriestoanalyzealleconomicfactorsofacompanyoramarketinordertocalcu-latethetruevalueofacommercialpaper,technicalanalystsassumethatallimportantinformationforthepaper’sfuturedevelopmentisalreadycontainedinitspastbehavior[3].Therefore,futuremovementscanbeanticipatedbythoroughlyanalyzingthestock’shistoryanditsinherentpatterns[4].Whiletheprinciplesofsomeofthetechniquesutilizedforatechnicalanalysisdatebacktothe18thcentury,theirvalidityhaspermanentlybeendisputed.Mostpopularly,theef cientmarkethypothesis[5]statesthat nancialmarketsareinformationallyef cient,and,therefore,allpastinformationisalreadycontainedineachstock’slastvalue.Asaresult,itisclaimedthattechniquesforatechnicalanalysiscannotperformbetterthanarandomwalkonthechartortheoveralldevelopmentofthemarket.Despiteallobjections,itstillwasnotpossibletoprooftheinvalidityoftechnicalanalysis,anditstechniquesaregainingpopularityamongboth,investorsandresearchers.
B.CharacteristicsofFinancialMarketData
The nancialinstrumentsusedforourworkaretwofu-tures,derivativeinstrumentstradedattheEuropeanderivativesexchangeEurex[6].Afuturescontractgivestheholdertheobligationtobuy(longposition)orsell(shortposition)aspeci edunderlyingassetatadistinctdateinthefutureandatapre-speci edprice.Thisdualitygivesthetraderthepossibilitytobene tfromrisingaswellasfromfallingmarketprices[7].
Aseverytransactioninamarketvariestheratioofsupplyanddemand,marketpricescanchangeinverysmallandir-regularintervals.Tofacilitateanalysis,thedataiscompressedintointervalsofacertainsize.Consequently,itispossibleto
notonlyidentifyasinglepriceforeachinterval,buttoextractadditionalinformation:Theopen,high,low,andclosepricesforthisinterval,namedOHLC-data(seeFig.
1).
Fig.1.Ontheleftsideweseethemarketrateofacertainequityduringoneday.Ontherightside,thesedatahavebeencompressedanddepictedusingtheso-calledcandlesticklayout:Theupperandlowershadowsmarktheday’shighestandlowesttradedprices,whereasthebodyofthecandlespansfromtheopentothecloseprice.Thecolorofthebodyillustratestheequity’sdevelopmentduringtheday:Ifthepricewentup,thebodyiswhiteandblackotherwise.