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29()Vol293JournalofHubeiNormalUniversity(NaturalScience)No3,2009谢明铎,吴加荣,何穗(华中师范大学数学与统计学院,湖北武汉430079):黄金市场是投资者管理者和经济管理学者共同关注的热点,自19世纪黄金市场建立以来,对黄金价格预测方法的研究一直是众多学者关注的焦点,随着黄金投资在中国的发展,其影响越来越大,深入了解其变化规律已经成为经济发展的迫切要求目前,已有大量的学者仅从定性角度研究了黄金价格的影响因素,但定量研究的文章较少主要是运用灰色马尔可夫预测法对黄金价格进行预测,考虑到重大事件的发生对黄金价格的影响,引入了虚拟变量,并基于上海黄金交易所提供的2008年1月9日到8月1日的数据对8月3日到10月31日12周内的黄金价格进行了预测:黄金价格;灰色马尔可夫预测法;投资风险;虚拟变量:O213.9:A:10092714(2009)03006005,,,,,200819,,,,,,,,,,,,,:,,,,,,1GM(1,1)GM(1,1),,,:(1983!),,,,.∀60∀,,,,GM(1,1),,,,,22.1GM(1,1)X(0)(k)(k=1,2,##p),X(1)(k+1)=X(0)(1)-ua(1)Y(k)=X(0)(k+1)=X(1)(k+1)-X(1)(k)(2)a,u,Y(k)kGM(1,1),Y(k)2.2Y(k),Y(k),Y(k),(Y(k)=X(0)(k+1)),n,Ai:Ai=(A1i,A2i)A1i=Y(k)+ai(3)A2i=Y(k)+bi(i=1,2,3,##n)(4)Y(k)k,A1i,A2i,Ai,AinA1i,A2i,2.3Pij=Mij(m)Mi(i,j=1,2,##,n)(5)Mij(m)Ai,mAj;MiAi:P(m)=P11(m)P12(m)#P1n(m)P21(m)P22(m)#P2n(m)####Pn1(m)Pn2(m)#Pnn(m)P(m)Pij(m)AimAj,P(m),P(1)Ak,P(1)k,maxjPkj(1)=Pk1(1),,AkA12.4,,A1i,A2i[A1i,A2i]Y∃(k):Y∃(k)=(A1i+A2i)/2(6)∀61∀(3),(4):Y∃(k)=Y(k)+(ai+bi)/2(7),,,,,,a(),,:Y%(k)=Y∃(k)+a*I[t&]3-,,1200819200881,30,,119,,200883~8112345678910(/g)207208.5207.23213.87209.54209.84213.35218.46224224.311121314151617181920(/g)222.4211.28205.34207210.26204.8200.08196.44197205.2721222324252627282930(/g)202.53197.36195.08196.58197.96206.11204.7212.03207.54202.523.1GM(1,1)3.1.1作AGO生成X(1)(k)=∋m=km=1X(0)(m),求得X(1)(k)如表22X(1)(k)k12345678X(1)(k)207415.5622.73836.61046.141259.691478.151702.35k910111213141516X(1)(k)1926.552150.852373.252584.532789.872996.873207.133411.93k1718192021222324X(1)(k)3612.013808.454005.454210.724413.254610.614705.694902.27k252627282930X(1)(k)5100.235306.345511.045723.075930.616133.133.1.2确定状态转移概率矩阵BYnB=-X(1)(!)+X(1)(2)21-X(1)(2)+X(1)(3)21##-X(1)(n-1)+X(1)(n)21Yn=X(0)(2)X(0)(3)#X(0)(n)BT=-311.25-519.12-729.66#-5617.05-5826.84-6031.87111#111YT=(208.5207.23213.87#212.03207.54202.52)3.1.3求参数A=[a,u]T=(BTB)-1BTYn:BTB=387570735.5-93811.98-93811.9829,BTYn=-1923127.166011.37,(BTB)-1BTYn=0.0026215.55∀62∀3.1.4确定GM(1,1)模型X(1)(k+1)=(X(0)(1)-ua)e-ak+ua=(207-215.550.0026)e-0.0026k+215.550.0026Y(k)=X(0)(k+1)=X(1)(k+1)-X(1)(k)=215.01e-0.0026kY(k)=215.01e-0.0026k1:Y(31)=198.363.2,,:A1:A11=Y(k)-10,A21=Y(k)-5A2:A12=Y(k)-5,A22=Y(k)A3:A13=Y(k),A23=Y(k)+5A4:A14=Y(k)+5,A24=Y(k)+10A5:A15=Y(k)+10,A25=Y(k)+15Y(k)kGM(1,1),GM(1,1)Y(k)2图1Y(k)=215.01e-0.0026k的图像图2状态划分图2,GM(1,1)3.32,A1A2A3A4A5M1=9,M2=7,M3=8,M4=2,M5=4A1A1A2A3A4A5:M11(1)=6,M12(1)=1,M13(1)=2,M14(1)=0,M15(1)=0,Mij(1),(ij=1,2,3,4,5)(5):P(1)=6/91/92/9002/72/73/70004/82/81/81/8001/201/2001/41/42/4,302008728~81A3,maxjP3j=P32=12,2008838A23.4R(1),2008848A2,[Y[31]-5,Y[31]][193.36,198.36](6),(7):Y∃(31)=Y(31)+-52=195.86/g;k=31,Y%=195.86/g;;k=31,Y%(k)=(195.86+a)/g(a)∀63∀4,3142(20088320081031),312GM(1,1)331~42GM31198.36195.86196.13-0.2732197.42189.92182.507.4233195.25179.75179.400.3534192.55182.55182.60-0.0535190.55179.55178.800.7536188.74173.24172.650.5937186.14177.64178.36-0.6838184.38186.88193.626.7439185.22192.77193.60-0.8340185.54185.54185.340.2041184.40179.90169.2410.6642181.27165.87166.50-0.63,129,,323841,8829,915,,10912,,,a,,GM(1,1),,GM(1,1),,,,,,,,,Au9999,,,,a,.:[1]EdwardP,KaoC.AnIntroductiontoStochasticProcesses[M].Beijing:ChinaMachinePress,1996.[2][M]:,1996[3]BLUEMENTHALRM,GETOORRK.MarkovProcessandPonrentialTheory[M].NewYork:AcademyPress,1986.[4]∀∀[M]:,2005.[5].[J].(B),2006,(06):75~77.[6][J],2008,(2):15~21[7],,[J],2006,12(27):8~11[8],[J],2007,(4):487~489[9],.[J].,2007,(22):23~27[10],!!![J],2005,(8):36~38(73)∀64∀:[1],.!!![M].:,2006.[2]VadimirN.Vapnik,,,[M].:,2000.[3]MartinBaxter,AndrewRennie.[M].:,2006.[4].[M].:,2005.[5].SPSS11.0()[M].:,2002.[6].[M].:,1999.[7].MATLAB[M].:,2005.[8],.300[J].,2007,(5):42~44.[9].[J].,2008,18(2):381~386.[10],.[J]..2005,14(2):176~181.Supportvectormachines-basedforecastinginShanghaiandShenzheng300indexYEYuan,HESui(CollegeofMathematicsandStatistics,HuazhongNormalUniversity,Wuhan430079,China)Abstract:BasedonthecharacteristicofthetimeseriesofShanghaiandShenzhen300index,proposedamethodwhichbasedoncombinationofPrincipalComponentAnalysis(PCA)andSupportVectorMachine(SVM).Firstly,extractthemaininformationofthefactorswhichinfluenceShanghaiandShenzhen300indexthroughPCA,thenSVMtotrainandforecast.Finally,inordertocomparepredictedvalueandtruevalue,wecalculatetheMeanSquareError(MSE)ofthepredictedclosingpriceintentimeperiods,whichis2.11617.Moreover,thebarchartofpredictedvalueandtruevaluetestifythatpredictedtrendisalmostaccurate.Therefore,itcanbeprovedthatusingSupportVectorMachinetopredictShanghaiandShenzhen300indexisfeasible.Keywords:ShanghaiandShenzhen300index;principalcomponentanalysis;supportvectormachine(64)TheforecastanalysisofgoldtradingmarketXIEMingduo,WUJiarong,HESui(CollegeofMathematicsandStatistics,HuazhongNormalUniversity,Wuhan430079,China)Abstract:sincethestockmarketwasestablishedinthe19thcentury,manyinvestors,mangersandscholarsfocusedontheresearchofgoldmarket,themodelofgoldpricesprojectionshasbeenthefocusofattentionofmanyscholars..Atpresent,alotofscholarsonlystudytheimpactofthepriceofgold,butlessquantitativeresearcharticleareavailableinourcou