用BP神经网络预测股票市场的涨跌

1BP2§2.1§2.2BP§2.3(MLP)§2.4BP§3.1§3.2§3.3§3.4§3.5§3.6§3.7BP3[1][2][3][4][5]BP96~99§3.1J§3.2§3.3§3.4§3.54§3.771.4%AbstractThemulti-layerfeedforwardback?propagationneuralnetwork(BPNeuralNetwork)hasfoundawidelyexpandingrangeofapplications.Itsstructureissimple,itworksstablyanditiseasytobeimplementedwithhardware.Thankstotheintroductionofhiddenlayersandnonlinearactivityfunctions,itcanaccomplishmanyfairlycomplicatedtasksofmodelclassifications.Thepredictionofstockmarketisoneofsuchproblems,forwhichsomestatisticalmodelshavebeendevelopedbutnotquitesuccessfully.Inthispaper,thegoodclassificationcapabilityofBPNeuralNetworksisutilizedtoforecasttheupsanddownsoftheShanghaiStockExchangeIndex.Basedonaresearchontheindexes,andaconsiderationoftheinfluencesofboththeshort-termandlong-termfactors,inputvectorsarecarefullyselectedandnormalized.Theon-linegradientdescentmethodisadoptedastheupdatingruleofweights.Thehidden-layerstructureofthenetworkshasbeenestablishedbya5newalgorithmcalledthe“prunemethod”.Theapplicationofacombinatorialpredictionmethodimprovesthereliabilityandaccuracyofthenetworktoacertainextent.Inlightofthenumericalresults,someshortcomingsoftheBPNeuralNetworksuchasslowconvergence,prematuresaturationandbadgeneralizationcapabilityhavebeenanalyzedandameliorated.OurworkshowsthattheimprovedBPNeuralNetworksarefeasibleandefficientfor,andmighthaveabrightfutureinthepredictionofthestockmarket.506FeedforwardNNsFeedbackNNsSelf-organizingNNsBP[7][29]BPBPBPBP7BP[1][2][3]BP[4][5]BPBPBP1.2.3.4.85.6.7.8.§2.11943W.McCullochW.PittsMP2-11949HebbHebb50601957RosenblattMP9i?2-2XORXOR101969GrossbergARTART1ART2ART31972KohonenSOMFukushimaNecognitronWerbosBPWidrowAdaline701982HopfieldHopfieldHNN1984HopfieldHNNHopfieldRumelhartMcClellandPDPPDP1986PDPBPBPKoskoHecht-NielsenBPHolland1986114Snowbirds19876SanDiego2000200INNS1988NeuralNetworks1988INNSIEEE19903IEEE809019881989199019911992IEEE§2.2BP1974Werbos[6]BPRumelhartMcClellandPDPBPXORTCBP12MLPXOR,2-3BP2-3BPBPLMS[7][32]BP23OiVj?kkjwjkjiWij?=(Ww)i=1,2,???Ij=1,2,???Jk=1,2,???K?P?=1,2,???P,g1g2?j???kKkjkjwh???12.2.1??k?kjkwkjj)()(111????kKkjkjjwghgV????2.2.21gSigmoidi13)(1111????kKkjkJjijjJjijiwgWVWH????????(2.2.3)ijWji))(()(11122????kKkjkJjijiiwgWgHgO??????2.2.42g?iO?ii=1?i2122)))(((21)(21)(??????jkkjkijiiiwgWgOE?????????2.2.5??i?t?t+1)(??E?Wwi???????PiiPOEE121)(21)()(????????2.2.6)(??E)(?Ep??~1g1g2SigmoidS0/1?1Sigmoid)exp(11)(xxg????)0(??(2.2.7)?)(xgtanh(x?))0(??(2.2.8)14242.2.824SSlogistic0,1SigmoidSigmoidSigmoid???????2.2.52.2.6?2.2.5W???????jiijijVWEW??????2.2.9?0))(('2??????iiiiOhg??(2.2.10w15???????????kjjkjjjkjkwVVEwEw????????????(2.2.11?????iiijjjWhg??)('12.2.12?=(Ww)??????oldnew2.2.13),(wW?????2.2.14???????PiiPOEE121)(21)()(??????????2.2.15??O??On-Line?2.2.5?25BP1625BPBPOn-LineBackPropagationAlgorithm1999[8]OGM)(?g?OGM2.2.617§2.3(MLP)Rn1957Kolmogorov1[9]nmRI?mmmI]1,0[?nmRI??:m2m+1nKolmogorov?[11],[30]CybenkoSigmoid2[10]GSigmoidN,,RCii??niRW?),,2,1(Ni??????????????NiiiiKXXWGCFF1),(?2.3.1)(nIC?),,,()(21nxxxX????)(nIC?0????????????NiiiiXWGCX1)()((2.3.2)2RnSigmoid181RRxG?:)(Sigmoid)(xGimx???1)(???xGimx?0)(????xGimx?)(xG????01)(xG00??xxRx?sgnSigmoid3[11])(xGSigmoid),,,()(21nxxxX????nRX?0???N,,RCii??niRW?),,2,1(Ni???????????NiiiiXWGCX1)()((2.3.3)23SigmoidFunahashiHornik4[12])(xGKnRN,,RCii??niRW?),,2,1(Ni??),,,()(21nxxxX????0????????????NiiiiXWGCX1)()(KxxxXn??),,,(21?(2.3.4)5[13])(xG)(X?nRK0???NniRW?Ni,,2,1??19?????????)()(1iiNiiXWGCXKxxxXn??),,,(21?(2.3.5))(X?6[14])(xG????????????NiiiiKXXWGCFF1),(?)(2nIL(nnRI?n)2?0),(2?????nIL????????nIiiNiidXXWGCX??21|)()(|(2.3.6)????nIdXX2122)|)(|()(?)(X?????dXXnI2|)(|)(X?Hornik[15]1993RiemannLeshno[16]Rn§2.420TakashiKKazuoABPTOPIX(TokyoStockExchangePricesIndexes))[17]Fujisu(Nikko)BullMarketBearMarket26261987TOPIXTOPIXtheFirstSectionoftheTokyoStockExchangeDow-JonesaverageTOPIX1.Vectorcurve2.Turnover3.Interestrate4.Foreignexchangerate5.NewYorkDow-Jonesaverage6.Others))1(/)((??tTOPIXtTOPIXnrt?,TOPIXttTOPIX????Niitirthope0)(??N21)(thope[0,1]threshold0.5????sellbuyoutput5.05.0??outputoutputoutputoutput012727m=4BPSigmoidBP19871~1989933TOPIX28buy-and-hold2819871TOPIX1.0019899buy-and-hold1.67predictionsystem221.98KamijoKTanigawaT[18]TOPIXtrianglepatternsJapanese-stylestockcharts29candlestickscharttop(bottom)resistanceline2923tCtAt1)1(????tttAssCA,)1()1(221?????????tttCssCsssC132?sstV~11~????ttttAAAVtHtLtttttAHAU??~ttttALAD??~ttDU~~ttLHtAtV~ttDU~~[0,1]tVtUtD67642444tVtUtDcontextlayer241?tV1?tU1?tD1?tSSS0.501615116152000tt-1,t-2???????????????????3.03.03.035.0111toutputtoutputtoutputoutputVVDDUUStS2.12.125*pattern(s)pername16151.06BPA3.1261998.6.15~1999.2.5161tA3.1?1?9?2?10?3?11?4?12?5?13?6?14?7?15?8?16k??kw?jk2.2.927wjkjVjwjk???k2.2.2-AA3.23.2?1?2??5?6??9?10??11?12??16A-1(0.1,0.15)(0.1,1)(0.1,1)(-0.1,0.1)B-1(0.1,0.15)(1,10)(1,10)(-0.1,0.1)C-1(0.1,0.15)(5,50)(1,10)(-0.1,0.1)D-1(0.1,0.15)(0.5,5)(0.5,5)(-0.1,0.1)E-12,3(0.5,5)(0.5,5)(-3,3)31MSE?=0.025?=0.01(-1,1)16-7-1P=100g1=tanh(x)g2=tanh(x)(2.2.6)MSE(MeanSquareError)VCR(ValidClassificationRatio)3128AAAEMSE?6??9C0(2.2.12)(2