基于Markov分析法的股票價(jià)格變化趨勢(shì)預(yù)測(cè)研究摘要本文主要應(yīng)用隨機(jī)過(guò)程中的Markov鏈及隱馬氏鏈模型（HMM模型）相關(guān)理論，以中國(guó)石油2007年11月5日至2021年2月26日，一共3230交易日的收盤價(jià)為研究對(duì)象，利用MATLAB軟件實(shí)現(xiàn)對(duì)股票價(jià)格變化趨勢(shì)的預(yù)測(cè)，并對(duì)股票的歷史價(jià)格數(shù)據(jù)進(jìn)行了分析，利用Markov分析法，構(gòu)造股票價(jià)格變動(dòng)的數(shù)學(xué)模型，給出股價(jià)未來(lái)的變化趨勢(shì)，研究了該Markov鏈的平穩(wěn)分布。鑒于Markov預(yù)測(cè)較適用于短期預(yù)測(cè)，本文進(jìn)一步利用HMM模型對(duì)該問(wèn)題進(jìn)行了更為細(xì)致地思考，利用該模型進(jìn)一步預(yù)測(cè)。對(duì)兩個(gè)模型的預(yù)測(cè)結(jié)果進(jìn)行了分析，并通過(guò)實(shí)例進(jìn)行了實(shí)證研究，最終表明Markov鏈預(yù)測(cè)，適用范圍較廣，HMM模型預(yù)測(cè)精度較高。關(guān)鍵詞：Markov鏈；MATLAB；股票價(jià)格；HMM模型；預(yù)測(cè)目錄TOC\o"1-3"\h\uTOC\o"1-3"\h\u6371摘要 Ⅰ69031緒論 ⑵HMM模型。首先在設(shè)置參數(shù)時(shí)，采用的時(shí)隨機(jī)產(chǎn)生的方式，通過(guò)不斷迭迭代產(chǎn)生的初始參數(shù)。如果對(duì)初始值優(yōu)化后在使用，一定會(huì)大大的降低運(yùn)算速度，使預(yù)測(cè)結(jié)果更加準(zhǔn)確。其次本文在訓(xùn)練時(shí)采用的Baum_Welch算法屬于EM算法的一種，存在局部最優(yōu)的問(wèn)題。故在今后的工作中應(yīng)該尋找更好的算法來(lái)訓(xùn)練參數(shù)從而得到最佳隱狀態(tài)數(shù)目。參考文獻(xiàn)[1]G.W.Morrison,D.H.Pike.KalmanFilteringAppliedtoStatisticalForecasting[J].Manag-ementScience,1977,23(7):768–774.[2]ChoiJ,LeeMandRheeM.Tradings&p500StockIndexFuturesUsingaNeural-Neuralnetwork[J].ProceedingsoftheThirdAnnualInternationalConferenceonArtificialIntelligenceapplicationsonWallStreet,1995,(2):63–72.[3]LeeK-E,LeeE-J,ParkH-S.UsingMarkovchainsofnucleotidesequencesasapossibleprecursortopredictfunctionalrolesofhumangenome:acasestudyoninactivechromatinregions.[J].Geneticsandmolecularresearch:GMR,2016,15(3).[4]NguyenN.AnAnalysisandImplementationoftheHiddenMarkovModeltoTechnologyStockPrediction[J].Risks,2017,5(4).Svoboda,Milan,Gangur,Mikulas.UsingofMarkovChainswithVaryingStateSpaceforPredictingShort-termoftheSharePriceMovements[J].MathematicalMeehodsinEconomics,2017.BaumLE,PetrieT.StatisticalInferenceforProbabilisticFunctionsofFiniteMarkovChains[J].AnnalsofMathematicalStatistics,1966,37(6):1544-1563.BaumLE,PetrieT,SoulesG,WeisN.AMaximizationTechniqueOccurringintheStatisticalAnalysisofProbabilisticFunctionsofMarkovChains[J].AnnalsofMathem-aticalStatistics,1970,41(1):164-171.BaumLE.Aninequalityandassociatedmaximizationtechniqueinstatisticalestimati-onofprobabilisticfunctionsofaMarkovprocess[J].Inequalities,1972’3:1-8.[9]RyanMS,NuddGR.TheViterbiAlgorithm[J].ProcIEEE,1973,61(5):268-278.[10]RabinerLR,JuangBH.AnintroductiontohiddenMarkovmodels[J].IEEEASSPMag,1986,3(1):4-16.SrivastavaA,KunduA,SuralS,MajumdarA.CreditCardFraudI3etectionUsingHiddenMarkovModel[J].IEEEtransactionsonDependable&SecureComputing,2008.5(1):37-48.KrishnalalG,RengarajanSB,SrinivasaganKG.ANewTextMiningApproachBasedonHMM-SVMforWebNewsClassifcation[J].InternationalJournalofComputerApplications,2010(19):98-104.HassanMR,NathB.StockmarketforecastingusinghiddenMarkovmodel-1:aNewapproach[C].InternationalConferenceonIntelligentSystemsDesign&Application,2005:192-196.SangHoPark,Ju-HongLee,Jae-WonSong,Tae-SuPark.ForecastingChangeDirect-ionsforFinancialTimeSeriesUsingHiddenMarkovModel.RS,2009:184-191.[15]CacciaM,RemillardAutoregressiveHiddenB.OptionPricingandHedgingforDiscreteTimeMarkovModel[J].LesCahiersduGERAD,2017.[16]李衛(wèi)民.ARMA-廣義回歸神經(jīng)網(wǎng)絡(luò)技術(shù)在股票預(yù)測(cè)中的應(yīng)用研究[D].山東科技大學(xué),2004.[17]盧瑞瑞.基于K-means聚類的馬氏鏈過(guò)程在股價(jià)趨勢(shì)預(yù)測(cè)中的應(yīng)用[D].華中科技大學(xué),2009.[18]武月,李紅春.基于AHP與馬氏鏈鏈的股票行情一類分析及預(yù)測(cè)[J].現(xiàn)代經(jīng)濟(jì)信息,2011,(22):190-191.[19]梁雪.一類約化信用風(fēng)險(xiǎn)模型的風(fēng)險(xiǎn)分析及應(yīng)用[D].蘇州大學(xué),2013.[20]許偉河.基于滾動(dòng)窗口馬氏鏈鏈預(yù)測(cè)模型的股票指數(shù)波動(dòng)情況研究[D].上海金融學(xué)院學(xué)報(bào),2014,(6):67-75.[21]王莉.基于人工智能算法的股票價(jià)格波動(dòng)規(guī)律預(yù)測(cè)方法研究[D].吉林大學(xué)2016.[22]CaiyunSun,QiyunMa,JiquanZhang,MoZhou,YananChen.PredictingseasonalfateofphenanthreneinaquaticenvironmentwithaMarkovchain[J].EnvironmentalScienceandPollutionResearch,2016,23(16):16661-16670[23]WenTsoHuang,ChengChangLu.AnenhancedabsorbingMarkovchainmodelforpredictingTAIEXIndexFutures[J].CommunicationsinStatistics-TheoryandMethods,2017,47(1):133-146.張冬青,韓玉兵,寧宣熙,劉雪妮.基于小波域隱馬爾可夫模型的時(shí)間序列分析-平滑、插值和預(yù)測(cè)[J].中國(guó)管理科學(xué),2008(02):122-127.朱嘉瑜,葉海燕,高鷹.基于隱馬爾可夫模型的股票價(jià)格預(yù)測(cè)組合模型[J].計(jì)算機(jī)工程與設(shè)計(jì),2009,30(21):余文利,廖建平,馬文龍.一種新的基于隱馬爾可夫模型的股票價(jià)格時(shí)間序列預(yù)測(cè)方法[J].計(jì)算機(jī)應(yīng)用與軟件,2010,27(06):186-190.[27]龔健.基于隱馬爾可夫鏈的證券價(jià)格模型及實(shí)證分析[D].復(fù)旦大學(xué),2011.[28]徐朱佳,謝銳,劉嘉,梅玉.隱馬爾可夫模型的改進(jìn)及其在金融預(yù)測(cè)中的應(yīng)用[J].工程數(shù)學(xué)學(xué)報(bào)，2017,34(5):470-480.[29]羅澤舉,朱思銘,何淼.基于隱馬爾可夫模型的多重序列分析[J].中山大學(xué)學(xué)報(bào)(自然科學(xué)版),2005(02).[30]閆新娟,譚敏生,嚴(yán)亞周,呂明娥.基于隱馬爾科夫模型和神經(jīng)網(wǎng)絡(luò)的入侵檢測(cè)研究[J].計(jì)算機(jī)應(yīng)用與軟件,2012,29(02):294-297.[31]于江德,樊孝忠,尹繼豪.隱馬爾可夫模型在自然語(yǔ)言處理中的應(yīng)用[J].計(jì)算機(jī)工程與設(shè)計(jì),2007(22).

附錄HMM模型建立的部分子程序如下:1.normalise.mfunction[M,z]=normalise(A,dim)ifnargin<2z=sum(A(:));s=z+(z==0);M=A/s;elseifdim==1z=sum(A);s=z+(z==0);M=A./repmatC(s,size(A,1),1);elsez=sum(A,dim);s=z+(z==0);L=size(A,dim);d=length(size(A));v=ones(d,l);v(dim)=L;c=repmat(s,v');M=A.Ic;end2.mk_stochastic.mfunction[T,Z]=mk_stochastic(T)if(ismatrix(T))&&(size(T,1)==1||size(T,2)==1)[T,Z]=normalise(T);elseifismatrix(T)Z=sum(T,2);S=Z+(Z==0);norm=repmat(S,1,size(T,2));T=T./norm;elsens=size(T);T=reshape(T,prod(ns(l:end-1)),ns(end));Z=sum(T,2);S=Z+(Z==O);norm=repmat(S,1,ns(end));T=T./norm;T=reshape(T,ns);end3.dhmm_emfunction[LL,prior,transmat,obsmat,nrIterations]=...dhmm_em(data,prior,transmat,obsmat,varargin)[max_iter,thresh,verbose,obs_prior_weight,adj_prior,adj_trans,adj_obs]=...process_options(varargin,'max_iter',10,'thresh',1e-4,'verbose',1,'obs_prior_weight',0,'adj_prior',1,'adj_trans',1,'adj_obs',1);previous_loglik=-inf;loglik=0;converged=0;num_iter=1;LL=[];if~iscell(data)data=num2cell(data,2);%eachrowgetsitsowncellendwhile(num_iter<=max_iter)&&~converged[loglik,exp_num_trans,exp_num_visits1,exp_num_emit]=...compute_ess_dhmm(prior,transmat,obsmat,data,obs_prior_weight);ifadj_priorprior=normalise(exp_num_visits1);endifadj_trans&&~isempty(exp_num_trans)transmat=mk_stochastic(exp_num_trans);endifadj_obsobsmat=mk_stochastic(exp_num_emit);endifverbose,fprintf(1,'iteration%d,loglik=%f/n',num_iter,loglik);endnum_iter=num_iter+1;converged=em_converged(loglik,previous_loglik,thresh);previous_loglik=loglik;LL=[LLloglik];endnrIterations=num_iter-1;4.dhmm_logprobfunction[loglik,errors]=dhmm_logprob(data,prior,transmat,obsmat)if~iscell(data)data=num2cell(data,2);endncases=length(data);loglik=0;errors=[];form=1:ncasesobslik=multinomial_prob(data{m},obsmat);[alpha,beta,gamma,ll]=fwdback(prior,transmat,obslik,'fwd_only',1);ifll==-inferrors=[errorsm];endloglik=loglik+ll;end5.process_optionsfunction[varargout]=process_options(args,varargin)n=length(varargin);if(mod(n,2))error('Eachoptionmustbeastring/valuepair.');endif(nargout<(n/2))