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1,2131.2002402.4102053.4100762008-11-2609JJ31291975-.....4312..TP274A1672-9102200902-0070-04...[1]......[2][3].[4][5]MLPGRNN..[6].....Vapnik———SVM[7].εSVR..[8].JournalofHunanUniversityofScience&TechnologyNaturalScienceEdition24220096Vol.24No.2Jun.200970.1εεfx.fxfx=w×x+bw∈Xb∈R.1wf.min12‖w‖2yi-w×xi-b≤εw×xi+b-yi≤εi=12…l‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖.22ξiξi*.min12‖w‖2+Cli=1Σξi+ξi*yi-w×xi-b≤ε+ξiw×xi+b-yi≤ε+ξi*ξiξi*≥0C0i=12…l‖‖‖‖‖‖‖‖‖Σ‖‖‖‖‖‖‖‖‖.3C.max-12li=1Σlj=1Σai-ai*aj-aj*·xi·xj-εli=1Σai+ai*+li=1Σyiai-ai*li=1Σai-ai*=0aiai*∈0C‖‖‖‖‖‖‖‖‖‖‖Σ‖‖‖‖‖‖‖‖‖‖‖.4.kxy=φx·φx.5max-12li=1Σlj=1Σai-ai*aj-aj*·kxixj-εli=1Σai+ai*+li=1Σyiai-ai*li=1Σai-ai*=0aiai*∈0C‖‖‖‖‖‖‖‖‖‖‖Σ‖‖‖‖‖‖‖‖‖‖‖.6w*=lj=1Σai-ai*·kxixj=0fx=lj=1Σai-ai*·kxix+b‖‖‖‖‖‖Σ‖‖‖‖‖‖.72IBM1990.10-1992.10.31990.10-1991.121992.1-1992.31992.4-1992.10.SVRMLPGRNN...45RDP-5RDP-10RDP-15RDP-20EMA155[9]1.RDP-nn.[10].EMAnnEMAn..RDP+553EMA3..[-11]..MSENMSEMAE.[11].2.1Tab.1InputandoutputvariblesEMA15RDP-5RDP-10RDP-15RDP-20pi-EMA15ipi-pi-5/pi-5×100pi-5-pi-10/pi-10×100pi-10-pi-15/pi-15×100pi-15-pi-20/pi-20×100RDP+5pi+5-pi/pi×100pi=EMA3iiEMAniipii71SVR.exp-γ·‖x-x'‖‖‖2...Cεγ..Cεγ.1.C=10ε=0.2γ=1.2.101091.MSE.MLP.SVR.MLP51..0.0090.0050.0031000.GRNNSVR.GRNN51..0.1.3.SVRMSENMSEMAE.SVRGRNNMLP.3...SVRGRNNMLP.234SVRMLPGRNNRDP+5.SVR.3.2Tab.2PerformancemeasuresandtheircalculationsMSE1nni=1Σyi-y赞i2NMSEmse/νaryMAE1nni=1Σyi-y赞ic=10MSE=0.0546MSE=0.0627MSE=0.070710.90.80.70.60.50.40.30.20.1epsilon1.11.21.31.41.51.61.71.81.92gamma1Fig.1Grid-searchonnyy赞3Tab.3PerformancemeasuresofSVRmodelandANNalgorithmsfortrainingandtestdataSVRMLPGRNNSVRMLPGRNNMSENMSEMAE0.04121.00240.16870.05631.47600.19530.05211.25650.18360.04881.07310.17080.06441.41840.20560.05841.28570.18490.60.40.20-0.2-0.4-0.6-0.80204060801001201401601802003MLPFig.3PredictedvaluesofMLPonthetestdataNomalizedtargetvalueTestdatapointspredictedvaluesactualvalues0.60.40.20-0.2-0.4-0.6-0.80204060801001201401601802002SVRFig.2PredictedvaluesofSVRonthetestdataNomalizedtargetvalueTestdatapointspredictedvaluesinSVRactualvalues720.60.40.20-0.2-0.4-0.6-0.80204060801001201401601802004GRNNFig.4PredictedvaluesofGRNNonthetestdataNomalizedtargetvalueTestdatapointspredictedvaluesactualvalues3IBMMLPGRNN.SVRMLPGRNN.GRNNMLP.SVR.SVRSVRSVR.[1]YaserSAMAtiyaAF.Introductiontofinancialforecasting[J].AppliedIntelligenceSpringer19966205-213.[2]BoxGEPJenkinsG.Timeseriesanalysisforecastingandcontrol[M].SanFranciscoHolden-Day1976.[3]HaykinsS.Neuralnetworksacomprehensivefoundation[M].NewYorkMacmillanCollegePublishingCompanyInc1994.[4]DorffnerG.Neuralnetworksfortimeseriesprocessing[J].NeuralNetworkWorldtheAcademyofSciencesoftheCzechRepublic199664447-468.[5]FrankRJDaveyNHuntSP.Inputwindowsizeandneuralnetworkpredictors[C]//IEEE-INNS-ENNSInternationalJointConferenceonNeuralNetworks2000Italy2000237-242.[6]MandicDPChambersJA.Recurrentneuralnetworksforprediction[M].UKWiley2001.[7]VapnikVN.Thenatureofstatisticallearningtheory[M].NewYorkSpringer1995.[8]ScholkopfBBurgesCJCSmolaAJ.Advancesinkernelmethods[M].LondonTheMITPress1999.[9]CaoLJTayFEH.Financialforecastingusingsupportvectormachines[J].NeuralComput&ApplicSpringer200110184-192.[10]ThomasonM.Thepractitionermethodsandtool[J].JournalofComputationalIntelligenceinFinanceAbsoluteBackorderService1999735-45.[11]PrincipeJEulianoNRLefebvreWC.Neuralandadaptivesystemsfundamentalsthroughsimulations[M].NewYorkJohnWiley&SonsInc1999.ModelofstockreturnspredictioncomparisonandselectionTANGLing-bing12SHENGHuan-ye1TANGLing-xiao31.DepartmentofComputerScienceandEngineeringShanghaiJiaoTongUniversityShanghai200240China2.DepartmentofComputerandElectronicEngineeringHunanBusinessCollegeChangsha410205China3.SchoolofEconomicsChangshaUniversityofScience&TechnologyChangsha410076ChinaAbstractComputationalFinanceisanewfieldwhichresearchapplicationsofMachineLearninginfinance.Stockreturnspredictionisimportantbranchoffinancewhichplayvitalimportantroleinfinancetoreduceriskandtakebetterdecisions.BasedontheoryofStatisticLearningandComputationalFinancethispaperdealswiththeapplicationofsupportvectorregressionSVRinstockreturnspredictiontosolvetheover-fittingproblemandgainagloballyoptimalsolution.ThroughselectingparametersbycrossvalidationthevalidityofSVRforstockreturnspredictionwereanalyzedthroughexperimentsonreal-worldstockdata.ItappearsthatSVRcandescribethecurvecharacteristicofnonstationarystocktimeserieswellandperformbetterthanboththemulti-layerperceptronMLPandthegeneralregressionneuralnetworksGRNN.4figs.3tabs.11refs.KeywordsStockreturnspredictionsupportvectorregressionSVRmulti-layerperceptronMLPgeneralregressionneuralnetworksGRNN.BiographyTANGLing-bingmalebornin1975Ph.D.lecturercomputationalfinance.73