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基于最小二乘小波支持向量机的股指波动率预测.docx

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基于最小二乘小波支持向量机的股指波动率预测 Title:PredictingStockIndexVolatilityBasedonLeastSquaresWaveletSupportVectorMachines Abstract: Stockindexvolatilitypredictionisofcrucialimportanceinfinancialmarketsforinvestorsandtraders.Inthisstudy,weproposeanovelmethodforforecastingstockindexvolatilitybasedonthecombinationofleastsquareswaveletanalysisandsupportvectormachines(SVMs).Theproposedapproachaimstocapturethenonlinearandnon-stationarycharacteristicsofstockmarketvolatility,allowingformoreaccuratepredictions.Empiricalresultsdemonstratetheeffectivenessofthemethodinimprovingvolatilityforecastingaccuracycomparedtotraditionalmodels. 1.Introduction Stockmarketvolatilityrepresentsthedegreeofpricefluctuationinfinancialmarkets,whichisessentialforinvestorswhenmakinginvestmentdecisionsandmanagingrisk.Accuratepredictionofstockindexvolatilityiscrucialformarketparticipantstooptimizetheirstrategiesandmaximizereturns.Traditionalmodelsforvolatilityprediction,suchasautoregressiveintegratedmovingaverage(ARIMA)andgeneralizedautoregressiveconditionalheteroskedasticity(GARCH),havelimitationsincapturingthenonlinearandnon-stationarynatureoffinancialtimeseriesdata.Toovercometheselimitations,weproposeanovelapproachbasedonleastsquareswaveletanalysisandsupportvectormachines. 2.Methodology 2.1.WaveletAnalysis Waveletanalysisisamathematicaltoolthatdecomposesasignalintodifferentfrequencycomponents,allowingforthedetectionofpatternsorfeaturesatdifferentscales.Inthisstudy,weusethediscretewavelettransform(DWT)todecomposethestockindexvolatilitytimeseriesintoapproximationanddetailcoefficients.TheDWTprovidesamultiscalerepresentationofthedata,whichenablestheidentificationofbothlong-termtrendsandshort-termfluctuations. 2.2.LeastSquaresWaveletSupportVectorMachines Leastsquareswaveletsupportvectormachines(LSWSVM)combinetheadvantagesofwaveletanalysisandSVMsforimprovedvolatilityprediction.LSWSVMutilizeswaveletcoefficientsasinputfeaturestobuildaregressionmodelusingSVMs.Theleastsquaresoptimizationtechniqueisemployedtoincorporatethet