Forecasting Financial Time Series with Support Vector Machin

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.

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