第9期 郑挺国等：基于极差的区制转移随机波动率模型及其应用 一 91- [11]Garman M,Klass M.On the estimation of security price volatilities from historical data[J].Joumal of Business,1980, 53:67-78. [12]Rogers L C G,Satchell S E.Estimating variance from high,low and closing prices[J].Annals of Applied Probability, 1991,1(4):504-512. [13]Yang D,Zhang Q.Drift-independent volatility estimation based on high,low,open,and closing prices[J].Journal of Business,2000,73:477-491. [14]唐勇，张世英.高频数据的加权已实现极差波动及其实证分析[J]·系统工程，2006,24(8)：52-57. Tang Yong,Zhang Shiying.Weighted realized range-based volatility based on high-frequency data and its empirical analysis [J].System Engineering,2006,24(8):52-57.(in Chinese) [15]Alizadeh S,Brandt M W,Diebold FX.Range-based estimation of stochastic volatility models[J].The Joumal of Finance, 2002,57(3):1047-1091. [16]Brandt M W,Diebold F X.A no-arbitrage approach to range-based estimation of retum covariance and correlations[J]. Journal of Business,2006,79:61-74. [17]Chou R.Forecasting financial volatilities with extreme values:The conditional autoregressive range(CARR)model[J]. Journal of Money,Credit and Banking,2005,37(3):561-582. [18]Li H,Hong Y.Financial volatility forecasting with range-based autoregressive volatility model[J].Finance Research Let- tes,2011,8(2):69-76. [19]周杰，刘三阳.条件自回归极差模型与波动率估计[J】.数量经济技术经济研究，2006，(9)：141-149. Zhou Jie,Liu Sanyang.Conditional autoregressive range model and estimation of volatilities[].The Journal of Quantitative Technical Economics,2006,(9):141-149.(in Chinese) [20]李红权，汪寿阳.基于价格极差的金融波动率建模：理论与实证分析[J].中国管理科学，2009,17(6)：1-8. Li Hongquan,Wang Shouyang.Modeling financial volatilities based on price range:Theoretical research and empirical study[J].Chinese Journal of Management Science,2009,17(6):1-8.(in Chinese) [21]蒋样林，吴晓霖，王春峰.基于日内价格幅度与回报的随机波动率模型[J].系统工程，2006,24(6)：68-73. Jiang Xianglin,Wu Xiaolin,Wang Chunfeng.Price-range and return based stochastic volatility model[J].System Engi- neering,2006,24(6):68-73.(in Chinese) [22]Lamoureux C G,Lastrapes W D.Persistence in variance,structural change,and the GARCH model[J].Journal of Busi- ness and Economic Statistics,1990,8(2):225-234. [23]Diebold F X,Inoue A.Long memory and regime switching[J].Joumal of Econometrics,2001,105(1):131-159. [24]Granger C WJ,Hyung N.Occasional structural breaks and long memory with an application to the S&P500 absolute stocke return[J].Journal of Empirical Finance,2004,11(3):399 -421. [25]Hamilton J D.A new approach to the economic analysis of nonstationary time series and the business cycle[J].Economet- ca,1989,57(2):357-384. [26]Hamilton J D,Susmel R.Autoregressive conditional heteroscedasticity and changes in regime[J].Joumal of Econometrics, 1994,64(1/2):307-333. [27]Cai J.A Markov model of switching-regime ARCH[J].Journal of Business and Economic Statistics,1994,12(3):309- 316. [28]Gary S F.Modeling the conditional distribution of interest rates as a regime-switching process[J].Journal of Financial Eco- nomics,1996,42(1):27-62. [29]蒋祥林，王春蜂，吴晓寐.基于状态转移ARCH模型的中国股市波动性研究[J].系统工程学报，2004,19(3)： 270-277 Jiang Xianglin,Wang Chunfeng,Wu Xiaolin.Investigating on volatility of Chinese stock market by regime-switching ARCH model[J].Journal of System Engineering,2004,19(3):270-277.(in Chinese) 万方数据第9期 郑挺国等：基于极差的区制转移随机波动率模型及其应用 一91一 [1 1]Garman M，Klass M．On the estimation of security price volatilities from historical data[J]．Joumal of Business，1980， 53：67—78． [12]Rogers L C G，SatcheU s E．Estimating variance from high，low and closing prices[J]．Annals of Applied Probability， 1991，1(4)：504—512． [1 3]Yang D，Zhang Q．Drift-independent volatility estimation based on high，low，open，and closing prices[J]．Journal of Business，2000，73：477—491． [14]唐勇，张世英．高频数据的加权已实现极差波动及其实证分析[J]．系统工程，2006，24(8)：52—57． Tang Yong，Zhang Shiying．Weighted realized range-based volatility based on high—frequency data and its empirical analysis [J]．System Engineering，2006，24(8)：52—57．(in Chinese) [15]Alizadeh S，Brandt M W，Diebold F X．Range-based estimation of stochastic volatility models[J]．The Joumal of Finance， 2002，57(3)：1047—1091． [16]Brandt M W，Diebold F X． A no-arbitrage approach to range-based estimation of return covariance and correlations[J]． Journal of Business，2006，79：61—74． [17]Chou R．Forecasting financial volatilities with extreme values：The conditional autoregressive range(CARR)model[J]． Journal of Money，Credit and Banking，2005，37(3)：561—582． [18]Li H，Hong Y．Financial volatility forecasting with range-based autoregressive volatility model[J]．Finance Research Let— ters，2011，8(2)：69—76． [19]周杰，刘三阳．条件自回归极差模型与波动率估计[J]．数量经济技术经济研究，2006，(9)：141—149． Zhou Jie，Liu Sanyang．Conditional autoregressive range model and estimation of volatilities[J]．The Journal of Quantitative ＆Technical Economics，2006，(9)：141—149．(in Chinese) [20]李红权，汪寿阳．基于价格极差的金融波动率建模：理论与实证分析[J]．中国管理科学，2009，17(6)：1—8． Li Hongquan，Wang Shouyang． Modeling financial volatilities based on price range：Theoretical research and empirical study[J]．Chinese Journal of Management Science，2009，17(6)：1—8．(in Chinese) [21]蒋祥林，吴晓霖，王春峰．基于日内价格幅度与回报的随机波动率模型[J]．系统工程，2006，24(6)：68—73． Jiang Xianglin，wu Xiaolin，Wang Chunfeng．Price-range and return based stochastic volatility model[J]．System Engi￾neering，2006，24(6)：68—73．(in Chinese) [22]Lamoureux C G，Lastrapes W D．Persistence in variance，structural change，and the GARCH model[J]．Joumal of Busi￾ness and Economic Statistics，1990，8(2)：225—234． [23]Diebold F X，Inoue A．Long memory and regime switching[J]．Journal of Econometrics，2001，105(1)：131—159． [24]Granger C W J，Hyung N．Occasional structural breaks and long memory with an application to the S&P 500 absolute stocke return[J]．Journal of Empirical Finance，2004，11(3)：399—421． [25]Hamihon J D．A new approach to the economic analysis of nonstationary time series and the business cycle[J]．Economet． rica，1989，57(2)：357—384． [26]Hamilton J D，Susmel R．Autoregressive conditional heteroscedasticity and changes in regime[J]．Joumal of Econometrics， 1994，64(1／2)：307—333． [27]Cai J．A Markov model of switching—regime ARCH[J]．Journal ofBusiness and Economic Statistics，1994，12(3)：309— 316． [28]Gary s F．Modeling the conditional distribution of interest rates as a regime—switching process[J]．Journal of Financial Eco— nomics，1996，42(1)：27—62． [29]蒋祥林，王春峰，吴晓霖．基于状态转移ARCH模型的中国股市波动性研究[J]．系统工程学报，2004，19(3)： 270—277． Jiang Xianglin，Wang Chunfeng，Wu Xiaolin．Investigating on volatility of Chinese stock market by regime—switching ARCH model[J]．Journal of System Engineering，2004，19(3)：270—277．(in Chinese) 万方数据