Forecasting Financial Time Series with Support Vector Machin(4)

1.0000

0.6727

1.0000

0.8027

1.0000

0.4829

Inasecondstep,wecomparedtheperformanceofSVMwithdifferentkernelfunctions.Fortheseexperiments,threedifferentdynamickernelfunctionstakenfrom[41]wereused:Thedynamictimewarpingkernel(DTW)aswellasthelongestcommonsubsequencekernelswithglobal(LCSS-global)aswellaslocalscaling(LCSSlocal).Asaresult,theDTW-kernelwasnotonlyconsiderablyfasterthanitsopponents.Duringthewholetraining,theLCSSkernelswerenotonceabletooutperformthepredictionaccuracyoftheDTWkernelonthetestdata(seeFig.4).Additionally,theLCSSkernelsappearedtorelyonspeci cattributes(features),whereastheDTWkernelshowedgoodresultsforalldatasets.ForthechoiceoftheSVMtype,weconductedclassi cationandregressionexperiments:Apartfromtheε-SVR(supportvectorregression)[42]andtheν-SVR[43],wemeasuredtheperformancefortheC-SVC(supportvectorclassi cation[44]andtheν-SVC[43].Insteadoftryingtopredictactualvalues,thesetechniquesweretrainedtoclassifythedataintotwocategories:oneforexpectedincreasing(rising),theanotheroneforexpecteddecreasing(falling)trends.Asaresult,wesawthatthepredictionresultsoftheν-SVRsigni cantlyoutperformedallothervariants,regardingbothMASE(forregressiontypes)andthehitrate,withtheε-SVRformulationrankingsecond.

Finally,weconductedsomeexperimentsinwhichwevariedthetotalamountandthelengthoftheinputtimeseriesoftheSVM.Con rmingtheobservationof[45],anincreaseintheamountofinputinformationdoesnotnecessarilyincreasethepredictionaccuracy.Instead,wecanseeinFig.4thatasmalleramountofcurrentinformationsigni cantlyimprovesthepredictionaccuracycomparedtoalargebacklogofhis-toricalinformation.C.MajorFindings

Fortheinputinformation,westatedthatthesheeramountofhistoricaldatadoesnotnecessarilyproducebetterresults.Instead,themainfocusshouldlieonthoroughpre-processingroutinestocapturetemporalpatternsofdifferentscale.Inthisregard,theappliedtechniqueofcreatingamulti-dimensionalvectorwithratesofchangeofdifferentmagnitudeworkedexceptionallywell.

Apartfromthat,ourresultsclearlyshowthehighabilityofSVMwithdynamickernelfunctionsintheareaof nancialtimeseriesforecasting.TheDTWkernelwasabletoproduceahitrateofupto70%overthewholehistoryofbothexaminedderivatives,comparedtoahitrateofonly47%forthenaiveforecast.Thisisevenmorerelevantasthehitratedirectlycorrelatestotheinputofcommonalgorithmictradingsystemsystems,triggeringactionswitheachtrendshift.

V.CONCLUSIONANDOUTLOOK

Inthisarticle,ashortintroductionintothe eldoftechnicalanalysisof nancialtimeserieshasbeengiven,andtheapplicationofSVMwithdynamickernelfunctionsinthisdomainhasbeenexamined.Aswedescribed,thedevelopedtechniquehasahighabilitytopredictfuturepricemovements

Fig.4.Thesegraphsshowsthedependenceofthepredictiononthesizeofthetimeslotusedeachtimeforpredictionandtraining:Theusedkernelfunctionsarefromlefttoright:DTW,LCSSglobal,andLCSSlocal.Theroundmarksinthediagramdenotetheresultswithatrainingsetof75periods,whereassquareandtriangularmarksshowtheresultsfor150and300periods.

ingdynamickernelfunctions,itispossibletouseawholerangeoftheprecedingseriesandanalyzeitasawholewiththeSVM’skernel.Aswecouldshow,thisapproachsigni cantlyincreasesthepredictionaccuracyandreliablyperformsbetterthanastandardnaiveforecast.

Forreal-worldexperimentsandapplicationsofthedevel-opedsystem,aninterfacetothetechnicalanalysissoftwareInvestox[46]wascreated(seeFig.5).Usingthisapplication,itbecomesnotonlypossibletoverifytheresultsonhistoricaldatausingavirtualbroker,butalsotoapplythesystemdirectlytocurrentdatainputsinaconstantlyevolvingmarketenvironment(seealso[47]).

Inourfutureresearch,theperformanceofthedevelopedsystemwillbeexaminedindifferenttradingconstellations.Contrarytotheworkonend-of-daydata,theperformanceofthetechniqueisalsohighenoughtouseitintheareaofintra-dayforecasting.Thisinvolvespredictionsinintervalsofonlyseveralminutes,ifnotjustinseconds’intervals.Inthisenvironmentofhighuncertaintyandconstanttrendshift,verydifferentrequirementsmayapply.Ontheotherhand,itisalsopossibletonotonlyusetheinputofonepre-processedtimeseries,buttocombinedifferentmarketpricesforpredictingacertainvalue.Thiskindofinter-marketanalysismayhavethepotentialtodetect uctuationsinaspeci cpriceandprematurelyratetheresultingin uenceonthetargetvalue.

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[3]R.Freedman,Introductionto nancialtechnology.Elsevier,2006.[4]L.Stevens,Essentialtechnicalanalysis:toolsandtechniquestospot

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