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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