统计与信息论坛 运用的困难。实证分析结果表明：对于此组数据，基 模型比基于极大似然估计(ML)方法估计GARCH 于马尔科夫蒙特卡罗(MCMC)方法估计的GARCH 模型更接近真值。 参考文献： [1]David Arida.Bayesain estimation of a markov-switching threshold asymmetric GARCH model with student-t innovations[J]. Econometrics Joumal,2008(1):1-22. [2]Teruo,Nakasuma.A Markov-Chain Sempling Algorithm for GARCH models[J].Studies in Nonlinear Dynamics& Econometrics,Berkeley Electronic Press,1998(2):46-53. [3]Teruo,Nakasuma.Bayesian analysis of ARMA-GARCH models:A Markov chain sampling approach[]].Joumal of Eoonometrics,2000(95):57-69. [4]陆懋祖.高等时间序列计量学[M].上海：上海人民出版社，1999：231-302. [5]Gelman A,Carlin J B,Stern HS,Rubin D B.Bayesian data analysis[M].CRC Press:London,1995:222-240. [6]Box GEP,Tiao GC.Bayesian inference in statistical analysis[M].Addison-Wesley:Reading,1973:340-367 [7]Carlin B P,LouisTA.Bayes and empirical bayes methods for data analysis[M].2nd ed.London:Chapman and Hall,2000: 231-302. [8]Hasting W K.Monte carlo sampling methods using markov chains and their applications(].Biometrica,1970(57):97-109. [9]Jonathan D.Cryer,Kung-Sik Chan.Time Series Analysis with Applications in R[M].New York:Springer,2001:331- 342. [10]Tiemey L.Markov chains for exploring posterior distributions[J].Annals of Statistics,1994(22):1701-1762. (贵任编辑：王南丰) The Estimation of GARCH Model Parameters Based on MCMC Algorithms PAN Hai-taol,WEN Xiao-ni2 (1.School of Statistics,Xi'an University of Finance and Eoonomics,Xi'an 710061,China; 2.School of Management,Xidian University,Xi'an 710061,China) Abstract:Traditional method is to use ML method to estimate the parameters,and ML method is essential- ly an optimization method.But GARCH model ordinarily has many constraints among parameters,which result in the failure of trust of MLE results.This paper use Markov Monte Carlo (MCMC)method to estimate the parameters of normal-based GARCH(1,1)model.The results based on MCMC are more reliable and we also show results based on MCMC are better than that of ML based by using real financial data. Key words:GARCH model;MCMC algorithm;Gibbs sampling;Metropolis -Hasting algorithm; volatility;forecasting 16 万方数据统计与信息论坛 运用的困难。实证分析结果表明：对于此组数据，基 于马尔科夫蒙特卡罗(MCMC)方法估计的GARCH 参考文献： 模型比基于极大似然估计(ML)方法估计GARCH 模型更接近真值。 [1]&丽d Arida．Bayesain estirIlation of ama如、，一s诵tching thr∞hdd asymmenic GARCH r∞dd诵也stud朗t．t inrK舰tionS[J]． Ec删trics Joumal。2008(1)：1—22． [2] Ten的，I、iak姻lrlla．A Md唧一Q面n s啪pling～鲥thm妇GARCH m硇els【J]．Studies in N袖near功咖遗& Ec踟帅etri鸥，酬ey Elea旺H1ic Pre鹞，1998(2)：46—53． [3]T印时，Nal【a双叻a．Bay鹳ian analysis of川RMA—GARCH mDdds：A Marl鼢，chain s锄pling appfoach[J]．．『a鼢a1 0f Ec雠trics，2000(95)：57—69． [4]陆懋祖．高等时间序列计量学[M]．上海：上海人民出版社，1999：23l一302． [5]Gdm锄A，Carlin J B，st锄H S，Rub．m D B．Bay菌锄data锄al酒s[M]．CRC Pr髑：Lond∞。1995：222—240． [6]BOX GE P，Ti∞G C。BayeSi孤infef朗ce irI statiStical anal姆s[M]．Addis∞一wesley：Re8diIlg，1973：340一367． [7]Cdin B P，L∞如T A．Bayes and唧idcal bay∞methods for data analySis[M]．2nd ed．k叽don：(、hpnm and H“，2000： 231—302． [8】HaSting wK．M。nte跚do sampling methods LtsiIlg markov c鼢nS and their applicationS[J]．Biofne伍ca，1970(57)：97—109． [9] Jonathan D．Cfy口，Kung—sik Cha工1．Time S萌皓AnalysiS诵th Applications iIl R[M]．New Y甜【：S研ng盯，2001：331— 342． [10] m咖ey L．～Iarl州c陆ns for唧嫡I】g p06td恼如tributiollS[J]．Anna】s of statiSti心，1994(22)：170卜1762． (责任编辑：王南车) ，nIe Esti眦ti蚰of Q堰CH ModeI Pa憎mete璐Based蚰M例C A120rith瞄 PAN Hai—taol。WEN Xia肛nP (1．Sch∞l 0f stat敏i∞，xi’柚U11iversi够0f R咖ce and Eo咖ics，)(i’锄710061，(Xm； 2．sch001 of M阻ag锄∞t，ⅪdiaJl Urliversi够，xi’锄710061，C扭m) Abstmct：7l、raditiom】method is to use ML method t0 eStinlate the parameters，and M[L meth()d is eSSlential． 1y a11 optimization method．But GARCH model ordimdly h弱many∞nSt商ntS锄ong pa埘neterS，which reSult in the fajlure of trust of Mu三results．This paper uSe Markov Monte Caurlo(MCMC)method t0 eStimate the parameterS of nonTla】一based GARCH(1，1)mOdel．T11e results based on MCMC are rnore reliable and、他also show results baSed on MCMC are better than that of ML b够ed by uSing real finaJlcial da乜． Key wordS：GARCH mDdel；MCMC algonthm；GibbS sarnpling；Met印oIis—HaSting a190rithm； v。latility；fc∞ecasting 16 万方数据