基于异质市场假说的中国股票市场已实现波动率特征研究
|
摘要
股市的波动及相关特征是国内外学者研究金融衍生工具的定价、有效资产组合的选择及金融风险管理的关键变量，也是金融学领域的一个研究热点。近年来，随着计算机及通讯技术的快速发展，极大的降低了数据记录和存储的成本，从而使得金融高频数据日益成为研究金融资产价格波动及市场微观结构的重要手段。Anderson和Bollerslev（1998）首次提出基于高频数据计算的“已实现”波动率，相比金融资产的日收益率，它能够更为精确的度量股票市场的波动。Cors（i2004）基于Müller等（1993）的异质市场假说理论提出了基于已实现波动率的异质自回归模型（Heterogeneous Auto-regressive model of Realized Volatility, HAR-RV模型)，它不属于真实长记忆类模型，而是一种简单的已实现波动率的可加时间序列模型，分别用不同时间段的已实现波动率来刻画特定类型市场参与者的交易对整个波动率的边际贡献，因而不仅具有明确的经济含义，也能用更简单的普通最小二乘OLS估计方法来刻画出已实现波动率的长记忆性等动态特征。
杠杆效应与量价关系是股票市场波动的两个主要特征，综合国内外对已实现波动率的研究现状，发现还没有文献在异质市场假说理论的基础上对已实现波动率的研究中同时考虑杠杆效应与量价关系。因此，本文旨在全面刻画股市波动特征和提高股市波动预测能力的同时，在HAR-RV模型的基础上，综合考虑波动的非对称性及量价关系，构建了LHAR-RV-V模型，并将其在中国股市进行实证分析，以进一步揭示中国股市波动的相关特征。实证结果表明该模型能够较好地捕捉我国股票市场波动的长记忆性和杠杆效应，且杠杆效应具有一定的持续性，从而进一步验证了Müller等（1993）提出的异质市场假说。此外，过去不同周期交易量的加入不仅能够更为细微的反映量价之间的关系，而且在一定程度上改善了模型的预测能力。
Volatility and its dynamics are central to asset and derivative pricing, effectiveportfolio choice and risk management, which has been a hot topic of finance area.Recently, with the rapid development of the computer and communicationtechnology, the cost of data recording and storing has been significantly reduced,which makes the high frequency data more availably for the research of the financialasset price volatility and the market microstructure. Andersen and Bollerslev(1998)kick-started a flurry of research on the use of high-frequency of intraday data formeasuring and forecasting daily volatility-“realized volatility(RV)”, compared to thedaily returns of the financial assets, the RV may measure the volatility moreprecisely. According to the heterogeneous market hypothesis proposed by Müller(1993), the Heterogeneous Auto-Regressive Realized Volatility model(HAR-RVmodel) has been proposed by Corsi(2004), utilized volatility components of differenttime resolutions derived from representing some different trade strategy of theparticular traders make their relevant yet marginal contribution on the wholevolatility to capture the empirical memory persistence of volatility in astraightforward and parsimonious manner. While its structure implies that it neverbelongs to a genuine long memory model, it possesses a well-defined economyimplication and can be estimated in a much simpler way-OLS.
Leverage effect and volume-volatility relations are the main characteristics ofthe stock market fluctuation. In this paper, we propose an extended version of theHAR model which considers both asymmetric responses of the realized volatility toprevious negative returns and the rice-volume relationship at all the consideredfrequencies, which has not been done by the extant researcher as far as the author’sknowledge, and we called it Leverage Heterogeneous Auto-Regressive RealizedVolatility with Volume model (LHAR-RV-V model). The proposed model is appliedto empirical analysis with the 1 minute high frequency data of Shenzhen 300 index.The empirical results show that the model can well capture the long memory and theleverage effect characteristics, and the leverage effect has certain sustainability. Inaddition, the past different cycle volume joined in the model can not only reflect therelationship between the volume and price in a more sophisticated way, but alsoimprove the predictive power of the model partly.
杠杆效应与量价关系是股票市场波动的两个主要特征，综合国内外对已实现波动率的研究现状，发现还没有文献在异质市场假说理论的基础上对已实现波动率的研究中同时考虑杠杆效应与量价关系。因此，本文旨在全面刻画股市波动特征和提高股市波动预测能力的同时，在HAR-RV模型的基础上，综合考虑波动的非对称性及量价关系，构建了LHAR-RV-V模型，并将其在中国股市进行实证分析，以进一步揭示中国股市波动的相关特征。实证结果表明该模型能够较好地捕捉我国股票市场波动的长记忆性和杠杆效应，且杠杆效应具有一定的持续性，从而进一步验证了Müller等（1993）提出的异质市场假说。此外，过去不同周期交易量的加入不仅能够更为细微的反映量价之间的关系，而且在一定程度上改善了模型的预测能力。
Volatility and its dynamics are central to asset and derivative pricing, effectiveportfolio choice and risk management, which has been a hot topic of finance area.Recently, with the rapid development of the computer and communicationtechnology, the cost of data recording and storing has been significantly reduced,which makes the high frequency data more availably for the research of the financialasset price volatility and the market microstructure. Andersen and Bollerslev(1998)kick-started a flurry of research on the use of high-frequency of intraday data formeasuring and forecasting daily volatility-“realized volatility(RV)”, compared to thedaily returns of the financial assets, the RV may measure the volatility moreprecisely. According to the heterogeneous market hypothesis proposed by Müller(1993), the Heterogeneous Auto-Regressive Realized Volatility model(HAR-RVmodel) has been proposed by Corsi(2004), utilized volatility components of differenttime resolutions derived from representing some different trade strategy of theparticular traders make their relevant yet marginal contribution on the wholevolatility to capture the empirical memory persistence of volatility in astraightforward and parsimonious manner. While its structure implies that it neverbelongs to a genuine long memory model, it possesses a well-defined economyimplication and can be estimated in a much simpler way-OLS.
Leverage effect and volume-volatility relations are the main characteristics ofthe stock market fluctuation. In this paper, we propose an extended version of theHAR model which considers both asymmetric responses of the realized volatility toprevious negative returns and the rice-volume relationship at all the consideredfrequencies, which has not been done by the extant researcher as far as the author’sknowledge, and we called it Leverage Heterogeneous Auto-Regressive RealizedVolatility with Volume model (LHAR-RV-V model). The proposed model is appliedto empirical analysis with the 1 minute high frequency data of Shenzhen 300 index.The empirical results show that the model can well capture the long memory and theleverage effect characteristics, and the leverage effect has certain sustainability. Inaddition, the past different cycle volume joined in the model can not only reflect therelationship between the volume and price in a more sophisticated way, but alsoimprove the predictive power of the model partly.
引文
[1]Andersen T G. Tim Bollerslev.Answering the Critics: Yes, ARCH Models DoProvide Good Volatility Forecasts[J]. International Economic Review,1998(4):885-905.
[2]Koopman.S J, Jungbacker.B, Hol.E.Forecasting Daily Variability of the S&P100Stock Index using historical, realized and implied volatility measurements[J].Journal of Empirical Finance,2005, 12 (3) : 445-475.
[3]魏宇.沪深300股指期货的波动率预测模型研究[J].管理科学学报.2010,13(2):66-76.
[4]Müller U, Dacorogna M,Dave R, Pictet O,Olsen R,Ward J.Fractals and intrinsictime–A challenge to econometricians[R]. Working paper, Olsen and Associates,1993.
[5]Corsi F. A Simple Long memory model of realized volatility[R]. Working Paper,University of Southern Switzerland, 2004,http://ssrn.com/abstract=626064.
[6]Corsi, F.A simple long memory model of realized volatility[J]. Journal ofFinancial Econometrics, 2009, 7(2), 174-196.
[7]Andersen T G. Tim Bollerslev, et.al.Exchange Rate Returns Standardized byRealized Volatility are (Nearly) Gaussian[J]. Multinational Finance Journal,2000 ,4 :159 - 179.
[8]Andersen T G,, Tim Bollerslev T, Diebold F .The distribution of exchange ratevolatility[J]. Journal of American Statistical Association, 2001,96:42-55.
[9]Andersen T. G.,Tim Bollerslev,et al.The Distribution of Stock ReturnVolatility [J]. Journal of Financial Economics, 2001 ,61:43-76.
[10]Andersen.T G, Bollerslev.T, Diebold.F X, Labys P.Modeling and forecastingrealized volatility[J]. Econometrica, 2003,71(2):579-625.
[11]Blair BJ, Poon SH, Taylor SJ.Forcasting S&P100 Volatility:The incrementalinformation content of implied volatility and high frequency index returns[J].Journal of Econometrics,2001,45(2):195-213.
[12]Martens, M., & Zein, J.Predicting financial volatility: High-frequency timeseries forecasts vis-` a-vis implied volatility[J]. Journal of Futures Markets,(2004)24, 1005–102.
[13]Koopman.S J, Jungbacker.B, Hol.E.Forecasting Daily Variability of the S&P100Stock Index using historical, realized and implied volatility measurements[J].Journal of Empirical Finance,2005, 12 (3):445-475.
[14]Choi K,Yu W, Zivot E.Long Memory versus Structural Breaks in Modeling andForecasting Realized Volatility[J]. Journal of International Money andFinance,2010,54(7):117-128.
[15]Granger C.W.J.,Joyeux R.An introduction to long-memory time series modelsand fractional differencing[J]. Journal of Time Series Analysis,1980,1(1):15-29.
[16]Hosking J.R.M.Fractional differencing[J]. Biometrika,1981,1(68):165-176.
[17]Nelson,D.B.Conditional Hetero-skedasticity in Asset Returns: A NewApproach[J]. Econometrica,1991, (59):347-370.
[18]Glosten,L.,Jagannathan,R.,and Runke,D.Relationship Between the ExpectedValue and the Volatility of the Nominal Excess Return on Stocks[J]. Journal ofFinance,1993,(48):1779-1801.
[19]RabemananjaraR.and J.M.Zakoian.Threshold ARCH Model sand Asymmetries involatility,Ch.11 in Nonlinear Dynamies, Chaos and Econometries[Z].M.H.Pesaran and S.M.Potter,New York:J.Wiley,1993.
[20]Baillie R F, Bollerslev T,Mikkelsen H O.Fractionally integrated generalizedautoregressive conditional heteroskedasticity[J]. Journal of Econometrics,1996,74(1):3-30.
[21]Fornari,F.,Mele,A.Sign and volatility-switching ARCH models: theory andapplication to international stock markets[J]. Journal of Applied Econometrics,1997.
[22]Corsi, Reno.HAR volatility modeling with heterogeneous leverage andjumps.2009.http://ssm.com/abstract=1316953.
[23]McAleer M, Medeiros MC.A multiple regime smooth transition HeterogeneousAutoregressive model for long memory and asymmetries[J]. Journal ofEconometrics,2008, 147:104-119.
[24]Louzis, Sisinisand ,Refenes.Forecasting stock index realized volatility with anAsymmetric HAR-FIGARCH model:The case of S&P500 and DJIA stockindices.2009.http://ssrn.com/abstract=1524861
[25]Chun Liu and John M Maheu.Intraday dynamics of volatility and duration:evidence from the Chinese stock market[R]. Working paper401, 2010.
[26]Andersen.T G, Bollerslev.T, Diebold.F X.Roughing it up:including jumpcomponents in the measurement ,modeling and forecasting of return volatility[R].Working paper.2005.
[27]Andersen.T G, Bollerslev.T, Diebold.F X.Roughing it up: including jumpcomponents in the measurement, modeling and forecasting of return volatility[J].Review of Economics and Statistics, 2005, 89(4),701-720.
[28]Barndorff-Nielsen O E,Shephard N.Power and bipower variation with stochasticvolatility and jumps[J]. Journal of Financial Econometrics,2004, (2):1-37.
[29]Corsi,F.,D.Pirino, and R.Ren`o.Discrete-time volatility forecasting withpersistent leverage effect and the link with continuous-time volatilitymodeling[R]. Working Paper,2010.
[30]Andersen,Bolleslev,Huang.A reduced form framework for modeling volatility ofspeculative prices based on realized variation measures[J]. Journal ofEconometrics,2011, (160):176-189.
[31]陈浪南,黄杰鲲.中国股票市场波动非对称性的实证研究[J].金融研究,2002,(5):67-73.
[32]李亚静,何跃,朱宏泉.中国股市收益率与波动性长记忆性的实证研究[J].系统工程理论与实践,2003, 1:9-15.
[33]房振明,王春峰,蒋祥林.中国股市回报波动性分析—高频数据揭示股市的特征[J].系统工程,2004, 2(22):13-19.
[34]张维,张小涛,熊熊.上海股票市场不对称研究—GJR模型与VS-GARCH模型的比较[J].数理统计与管理.2005,(11):96-102.
[35]张维,张永杰.异质信念、卖空限制与风险资产价格[J].管理科学学报,2006,(4):58-64.
[36]蒋天虹.我国股票市场波动非对称效应的反转[J].当代财经,2008, (2):65-68.
[37]陈国进,张贻军.异质信念、卖空限制与我国股市的暴跌现象研究[J].金融研究,2009, (4):80-91.
[38]黄后川,陈浪南.中国股票市场波动率的高频估计与特性分析[J].经济研究,2003, (2):74-84.
[39]徐正国,张世英.调整“已实现波动率”与GARCH及SV模型对波动的预测能力的比较研究[J].系统工程,2004,(22):60-63.
[40]徐国正,张世英.多维高频数据的“已实现”波动建模研究[J].系统工程学报，2006, 21（1）：6-11.
[41]张波,钟玉洁,田金方.基于高频数据的沪指波动的长记忆性驱动因素分析[J].统计与信息论坛,2009, 24(6):21-26.
[42]唐勇,池云果.基于已实现波动率的长记忆性分析[J].福州大学学报（哲学社会科学版）,2010, 5:27-32.
[43]曾增展.基于高频数据股票市场已实现波动率预测研究[D].中国台湾,2009.
[44]Merton R．C.On Estimating the expected return on the market：all exploratoryinvestigation[J]. Journal ofFinancial Economics,1980, 8:323-361.
[45]Engle.R F, Russell J.R.Autoregressive Conditional Duration: A New Model forIrregularly Spaced Transaction Data[J]. Econometrica, 1998, (66), 1127-1162 .
[46]Mcinish T．H．，Wood，R.A．，Intraday and overnight retums and day-of-the·weekeffect[J]. Journal of Financial Research,1985, 8:119-126.
[47]AnatR Admati，Paul Pfleiderer.A Theory of Intraday Patterns：Volume and PriceVariability[J]. The review ofFinancial Studies, 1988, l(1):3-40．.
[48]Brock W. A.,KlcidonA.W.Periodic market closure and trading volume[J].Journal of Economic Dynamic and Control, 1992, 16:451-489.
[49]Andersen, T.G.,.Return volatility and trading volume: an information flowinterpretation of stochastic volatility[J]. Journal of Finance, 1996 (51): 169-204.
[50]Andersen, T.G., Bollerslev, T,.Heterogeneous information arrivals and returnvolatility dynamics: uncovering the long-run in high frequency returns[J].Journal of Finance, 1997 (52): 975-1005.
[51]Andersen T．Q，Bollerslev T．，Cai J.Intraday and interday volatility in theJapanese stock market[J]. Journal ofIntea'national Markets, 2000,.10:107-130.
[52]Goodhart C．and Figliuoli L.Every minute counts in financial markets[J]. Journalof International Money and Finance, l991, 10:23-52.
[53]Bollerslev, Timand Domowitz.Trading Patterns and Price in the InterbankForeign Exchange Market[J]. Journal of Finance, 1993, 48:1421-1443.
[54]Stankewich,C.J.;Chapman,Jens;Muthusamy,Raman.Relationship of mechanicalfactors to the strength of proximal femur fractures fixed with cancellousscrews[J]. Journal of orthopaedic trauma,1996, 10(4):248-257.
[55]Ebens H.Realized Stock Volatility[M]. The Johns Hopkins University, 1999.
[56]唐勇.基于高频数据的金融市场分析[ D ] .天津:天津大学,2007.
[57]徐正国,张世英.高频时间序列的改进“已实现”波动特性与建模[J].系统工程学报.2005, 20(4):344-350.
[58]Andersen.T G, Bollerslev.T, Diebold.F X, Labys P.Modeling and forecastingrealized volatility[J]. Econometrica, 2003,71(2):579-625.
[59]Baillie R F, Bollerslev T, Mikkelsen H O.Fractionally integrated generalizedautoregressive conditional heteroskedasticity[J]. Journal of Econometrics,1996,74(1):3-30.
[60]Engle R. F. and T. Bollerslev.Modeling the Persistence of Conditional Variances[J]. Econometric Reviews , 1986 (5):1-50.
[61]王春峰,郑仲民,房振明.中国股市已实现“核”波动研究[J].北京理工大学学报(社会科学版),2011, 13(3):11-26.
[62]Barndorff-Nielsen O E P R Hansen A Lunde N Shephard.Designing realisedkernel to measure the ex-post variation of equity prices the presence of noise[J].Econometrica, 2008 (11):1481-1536.
[63]Barndorff-Nielsen, Peter R. Hansen, Asger Lunde and Neil Shephard.DesigningRealised Kernels to Measure the ex-post Variation of Equity Prices in thePresence of Noise,Econometrica[J]. Forthcoming,2008.
[64]汤果,何晓群,顾岚.FIGARCH模型对股市收益长记忆性的实证研究[J].统计研究,1999(7):39-42.
[65]庞淑娟,刘向丽,汪寿阳.中国期货市场高频波动率的长记忆性[J].系统工程理论与实践,2011, 6(31):1039-1044.
[66]梁丽珍,王茂斌,孔东民.交易冲击与资产的非对称波动：基于“已实现波动率”[J].金融评论.2010, (3):73-85.
[67]Calvet L. E. and A. J. Fisher.Multifractality in Asset Returns: Theory andEvidence [J]. The Review of Economics and Statistics, 2002, 84(3):381-406.
[68]LeBaron B.Stochastic volatility as a simple generator of apparent financialpower laws and long memory[J]. Quantitative Finance, 2001,1(6):621-631.
[69]张伟.基于已实现波动率的中国股票市场异质性的实证研究[D].成都：电子科技大学, 2007.
[70]Clark P K.A subordinated stochastic process model with finite variance forspeculative prices[J]. Econometrica, 1973, 41: 135-155.
[71]Zumbach, G. O. and Lynch, P.:Heterogeneous volatility cascade in financialmarkets[J]. Physica ,2001.
[72]Müller U,Dacorogna M,Dave R,Olsen R,Pictet O,Weizsacker J.Volatilities ofdifferent time resolutions-analyzing the dynamics of market components[J].Journal of Empirical Finance,1997, 4(2):213-239.
[73]文凤华,唐海如,刘晓群.中国证券市场HAR-BACD-V模型及其应用[J].系统工程理论与实践, 2012,32(3):608-613.
[74]Mandelbrot B.The Fractal Geometry of Nature[M]. W.H. Freeman andCompany,New York. 1983.
[75]Pictet O,Dacorogna M,Müller U,Olsen R,Ward J.Real-time trading models forforeign exchange rates[J]. Neural NetworkWorld,1992, 2(6):713–744.
[76]Copeland T E.A model of asset trading under the assumption of sequentialinformation arrival[J]. Journal of Finance, 1976, 31:1149-1168.
[77]Morse D.Asymmetric information in securities markets and trading volume[J].Journal of Financial and Quantitative Analysis, 1980,15:1129-1148.
[78]Karpoff. J. M.Costly Sales and the Correlation of Returns with Volume[R].Working Paper. 1985,University of WA.
[79]Robert H. Jennings, Christopher B. Barry.Information Dissemination andPortfolio Choice[J]. Journal of Financial and Quantitative Analysis,1983,18(1):1-19.
[80]Beaver,William,Lambert,Richard,Morse.The information content of securityprices[J]. Journal of Accounting and Economics, 2001, 2:-28.
[81]Epps. T. W and M. L. Epps.The Stochastic dependence of Security priceschanges and transaction volumes: implications for the mixture of distributionshypothesis[J]. Econometrica,1976, 44:305-321.
[82]Tauchen,Q. and M. Pitts.The price variability-volume relationship on thespeculative markets[J]. Econometrica,1983, 5 (1): 485-505.
[83]Harris, L.D.Conservation corridors: A highway system for wild- life. ENFOReport 85-5. Environmental Information Center of the Florida ConservationFoundation, Inc., Winter Park, FL; 1985.
[84]Torben G Andersen.Return volatility and trading volume：an information flowinterpretation of stochastic volatility[J]. Journal of finance,1996,7(1):169-204.
[85]Roman Liesenfeld.A generalized bivariate mixture model for stock pricevolatility and trading volume[J]. Journal of Econometrics, 2001,104:141-178.
[86]Lamoureux C G, Lastrapes W D.Heteroskedasticity in stock return data volumeversus GARCH effects[J]. Joural of Finance, 1990,45:221-229.
[87]Ane T, Geman N.Order flow, transaction clock and normality of asset returns[J].Journal of Finance, 2000, 55:2259-2284.
[88]吴冲锋,吴文峰.基于成交量的股价动力学分析方法[J].系统工程理论方法应用,2001, 10(1):1-7.
[89]吴冲锋,王承炜,吴文峰.交易量和交易量驱动的股价动力学分析方法[J].管理科学学报, 2002, 5(1):1-11.
[90]王承炜,吴冲锋.中国股市价格-交易量的线性及非线性因果关系研究[J].管理科学学报,2002, 5(4):7-12.
[91]李双成,邢志安,任彪.基于MDH假说的中国沪深股市量价关系实证研究[J].系统工程,2006, 24(4):77-82,
[92]耿克红,张世英.金融市场超高频时间序列ACD-GARCH-V模型研究[J].统计与决策,2007 (2):81-83,
[93]Craig A·Depken.Good Bad News and GARCH Effects in Stock Return Data[J].Journal of Applied Economics,1999, (2): 313~327.
[94]凌士勤,杨波,袁开洪.分类信息对股市波动的影响研究[J].中国管理科学,2005, 13 (3):20-25.
[95]凌士勤.异强度分类信息冲击的EGARCH效应研究[J].工业技术经济,2009,28(1):94-98.
[96]Forsberg, L., and E. Ghysels. Why do absolute returns predict volatility sowell[J]. Journal of Financial Econometrics, 2007, 5(1), 31-67
[97]刘向丽,汪寿阳,洪永淼.基于ACD模型的中国期货市场波动性分析[M].科学出版社, 2010:114-123.
[98]房振明,王春峰,蒋祥林.中国股市回报波动性分析——基于高频数据揭示股市的特征[J].系统工程,2004, 22(2):13-19.
[99]Manganelli,S.Duration, volume and volatility impact of trades[J]. Journal ofFinancial Markets, 2005,8:377-399.
[1]Andersen T G. Tim Bollerslev.Answering the Critics: Yes, ARCH Models Do Provide Good VolatilityForecasts [J]. International Economic Review, 1998(4):885-905.
[2]Koopman.S J, Jungbacker.B, Hol.E.Forecasting Daily Variability of the S&P100 Stock Index usinghistorical, realized and implied volatility measurements [J]. Journal of Empirical Finance,2005, 12(3) : 445-475.
[3]魏宇.沪深300股指期货的波动率预测模型研究[J].管理科学学报.2010,13(2):66-76.
[4]Müller U, Dacorogna M,Dave R, Pictet O,Olsen R,Ward J.Fractals and intrinsic time–A challenge toeconometricians[R]. Working paper, Olsen and Associates, 1993.
[5]Corsi F. A Simple Long memory model of realized volatility[R]. Working Paper, University ofSouthern Switzerland, 2004,http://ssrn.com/abstract=626064.
[6]Corsi, F.A simple long memory model of realized volatility[J]. Journal of Financial Econometrics,2009, 7(2), 174-196.
[7]Andersen T G. Tim Bollerslev, et.al.Exchange Rate Returns Standardized by Realized Volatility are(Nearly) Gaussian[J]. Multinational Finance Journal, 2000 ,4 :159 - 179.
[8]Andersen T G,, Tim Bollerslev T, Diebold F .The distribution of exchange rate volatility[J]. Journalof American Statistical Association, 2001,96:42-55.
[9]Andersen T. G.,Tim Bollerslev,et al.The Distribution of Stock Return Volatility [J]. Journal ofFinancial Economics，2001 ,61:43-76.
[10]Andersen.T G, Bollerslev.T, Diebold.F X, Labys P.Modeling and forecasting realized volatility[J].Econometrica, 2003,71(2):579-625.
[11]Blair BJ, Poon SH, Taylor SJ.Forcasting S&P100 Volatility:The incremental information content ofimplied volatility and high frequency index returns[J]. Journal of Econometrics,2001,45(2):195-213.
[12]Martens, M., & Zein, J.Predicting financial volatility: High-frequency time series forecasts vis-`a-vis implied volatility.[J]. Journal of Futures Markets, (2004)24, 1005–102.
[13]Koopman.S J, Jungbacker.B, Hol.E.Forecasting Daily Variability of the S&P100 Stock Index usinghistorical, realized and implied volatility measurements [J]. Journal of Empirical Finance,2005, 12(3) : 445-475.
[14]Choi K,Yu W, Zivot E.Long Memory versus Structural Breaks in Modeling and ForecastingRealized Volatility[J]. Journal of International Money and Finance,2010,54(7):117-128.
[15]Granger C.W.J.,Joyeux R.An introduction to long-memory time series models and fractionaldifferencing[J]. Journal of Time Series Analysis,1980,1(1):15-29.
[16]Hosking J.R.M.Fractional differencing[J]. Biometrika,1981,1(68):165-176.
[17]Nelson,D.B.Conditional Hetero-skedasticity in Asset Returns: A New Approach[J].Econometrica,1991, (59):347-370.
[18]Glosten,L.,Jagannathan,R.,and Runke,D.Relationship Between the Expected Value and theVolatility of the Nominal Excess Return on Stocks[J]. Journal of Finance,1993,(48):1779-1801.
[19]RabemananjaraR.and J.M.Zakoian.Threshold ARCH Model sand Asymmetries in volatility,Ch.11 inNonlinear Dynamies, Chaos and Econometries[Z]. M.H.Pesaran and S.M.Potter,NewYork:J.Wiley,1993.
[20]Baillie R F, Bollerslev T,Mikkelsen H O.Fractionally integrated generalized autoregressiveconditional heteroskedasticity[J]. Journal of Econometrics,1996, 74(1):3-30.
[21]Fornari,F.,Mele,A.Sign and volatility-switching ARCH models: theory and application tointernational stock markets[J]. Journal of Applied Econometrics, 1997.
[22]Corsi, Reno.HAR volatility modeling with heterogeneous leverage andjumps.2009.http://ssm.com/abstract=1316953.
[23]McAleer M, Medeiros MC.A multiple regime smooth transition Heterogeneous Autoregressivemodel for long memory and asymmetries[J]. Journal of Econometrics,2008, 147:104-119.
[24]Louzis, Sisinisand ,Refenes.Forecasting stock index realized volatility with an AsymmetricHAR-FIGARCH model:The case of S&P500 and DJIA stockindices.2009.http://ssrn.com/abstract=1524861
[25]Chun Liu and John M Maheu.Intraday dynamics of volatility and duration: evidence from theChinese stock market[R]. Working paper401, 2010.
[26]Andersen.T G, Bollerslev.T, Diebold.F X.Roughing it up:including jump components in themeasurement ,modeling and forecasting of return volatility[R]. Working paper.2005.
[27]Andersen.T G, Bollerslev.T, Diebold.F X.Roughing it up: including jump components in themeasurement, modeling and forecasting of return volatility[J]. Review of Economics and Statistics,2005, 89(4),701-720.
[28]Barndorff-Nielsen O E,Shephard N.Power and bipower variation with stochastic volatility andjumps[J]. Journal of Financial Econometrics,2004, (2):1-37.
[29]Corsi,F.,D.Pirino, and R.Ren`o.Discrete-time volatility forecasting with persistent leverage effectand the link with continuous-time volatility modeling[R]. Working Paper,2010.
[30]Andersen,Bolleslev,Huang.A reduced form framework for modeling volatility of speculative pricesbased on realized variation measures[J]. Journal of Econometrics,2011, (160):176-189.
[31]陈浪南,黄杰鲲.中国股票市场波动非对称性的实证研究[J].金融研究,2002, (5):67-73.
[32]李亚静,何跃,朱宏泉.中国股市收益率与波动性长记忆性的实证研究[J].系统工程理论与实践,2003, 1:9-15.
[33]房振明,王春峰,蒋祥林.中国股市回报波动性分析—高频数据揭示股市的特征[J].系统工程,2004, 2(22):13-19.
[34]张维,张小涛,熊熊.上海股票市场不对称研究—GJR模型与VS-GARCH模型的比较[J].数理统计与管理.2005,(11):96-102.
[35]张维,张永杰.异质信念、卖空限制与风险资产价格[J].管理科学学报,2006, (4):58-64.
[36]蒋天虹.我国股票市场波动非对称效应的反转[J].当代财经,2008, (2):65-68.
[37]陈国进,张贻军.异质信念、卖空限制与我国股市的暴跌现象研究[J].金融研究,2009, (4):80-91.
[38]黄后川,陈浪南.中国股票市场波动率的高频估计与特性分析[J].经济研究,2003, (2):74-84.
[39]徐正国,张世英.调整“已实现波动率”与GARCH及SV模型对波动的预测能力的比较研究[J].系统工程,2004,(22):60-63.
[40]徐国正,张世英.多维高频数据的“已实现”波动建模研究[J].系统工程学报，2006, 21（1）：6-11.
[41]张波,钟玉洁,田金方.基于高频数据的沪指波动的长记忆性驱动因素分析[J].统计与信息论坛,2009, 24(6):21-26.
[42]唐勇,池云果.基于已实现波动率的长记忆性分析[J].福州大学学报（哲学社会科学版）,2010,5:27-32.
[43]曾增展.基于高频数据股票市场已实现波动率预测研究[D].中国台湾,2009.
[2]Koopman.S J, Jungbacker.B, Hol.E.Forecasting Daily Variability of the S&P100Stock Index using historical, realized and implied volatility measurements[J].Journal of Empirical Finance,2005, 12 (3) : 445-475.
[3]魏宇.沪深300股指期货的波动率预测模型研究[J].管理科学学报.2010,13(2):66-76.
[4]Müller U, Dacorogna M,Dave R, Pictet O,Olsen R,Ward J.Fractals and intrinsictime–A challenge to econometricians[R]. Working paper, Olsen and Associates,1993.
[5]Corsi F. A Simple Long memory model of realized volatility[R]. Working Paper,University of Southern Switzerland, 2004,http://ssrn.com/abstract=626064.
[6]Corsi, F.A simple long memory model of realized volatility[J]. Journal ofFinancial Econometrics, 2009, 7(2), 174-196.
[7]Andersen T G. Tim Bollerslev, et.al.Exchange Rate Returns Standardized byRealized Volatility are (Nearly) Gaussian[J]. Multinational Finance Journal,2000 ,4 :159 - 179.
[8]Andersen T G,, Tim Bollerslev T, Diebold F .The distribution of exchange ratevolatility[J]. Journal of American Statistical Association, 2001,96:42-55.
[9]Andersen T. G.,Tim Bollerslev,et al.The Distribution of Stock ReturnVolatility [J]. Journal of Financial Economics, 2001 ,61:43-76.
[10]Andersen.T G, Bollerslev.T, Diebold.F X, Labys P.Modeling and forecastingrealized volatility[J]. Econometrica, 2003,71(2):579-625.
[11]Blair BJ, Poon SH, Taylor SJ.Forcasting S&P100 Volatility:The incrementalinformation content of implied volatility and high frequency index returns[J].Journal of Econometrics,2001,45(2):195-213.
[12]Martens, M., & Zein, J.Predicting financial volatility: High-frequency timeseries forecasts vis-` a-vis implied volatility[J]. Journal of Futures Markets,(2004)24, 1005–102.
[13]Koopman.S J, Jungbacker.B, Hol.E.Forecasting Daily Variability of the S&P100Stock Index using historical, realized and implied volatility measurements[J].Journal of Empirical Finance,2005, 12 (3):445-475.
[14]Choi K,Yu W, Zivot E.Long Memory versus Structural Breaks in Modeling andForecasting Realized Volatility[J]. Journal of International Money andFinance,2010,54(7):117-128.
[15]Granger C.W.J.,Joyeux R.An introduction to long-memory time series modelsand fractional differencing[J]. Journal of Time Series Analysis,1980,1(1):15-29.
[16]Hosking J.R.M.Fractional differencing[J]. Biometrika,1981,1(68):165-176.
[17]Nelson,D.B.Conditional Hetero-skedasticity in Asset Returns: A NewApproach[J]. Econometrica,1991, (59):347-370.
[18]Glosten,L.,Jagannathan,R.,and Runke,D.Relationship Between the ExpectedValue and the Volatility of the Nominal Excess Return on Stocks[J]. Journal ofFinance,1993,(48):1779-1801.
[19]RabemananjaraR.and J.M.Zakoian.Threshold ARCH Model sand Asymmetries involatility,Ch.11 in Nonlinear Dynamies, Chaos and Econometries[Z].M.H.Pesaran and S.M.Potter,New York:J.Wiley,1993.
[20]Baillie R F, Bollerslev T,Mikkelsen H O.Fractionally integrated generalizedautoregressive conditional heteroskedasticity[J]. Journal of Econometrics,1996,74(1):3-30.
[21]Fornari,F.,Mele,A.Sign and volatility-switching ARCH models: theory andapplication to international stock markets[J]. Journal of Applied Econometrics,1997.
[22]Corsi, Reno.HAR volatility modeling with heterogeneous leverage andjumps.2009.http://ssm.com/abstract=1316953.
[23]McAleer M, Medeiros MC.A multiple regime smooth transition HeterogeneousAutoregressive model for long memory and asymmetries[J]. Journal ofEconometrics,2008, 147:104-119.
[24]Louzis, Sisinisand ,Refenes.Forecasting stock index realized volatility with anAsymmetric HAR-FIGARCH model:The case of S&P500 and DJIA stockindices.2009.http://ssrn.com/abstract=1524861
[25]Chun Liu and John M Maheu.Intraday dynamics of volatility and duration:evidence from the Chinese stock market[R]. Working paper401, 2010.
[26]Andersen.T G, Bollerslev.T, Diebold.F X.Roughing it up:including jumpcomponents in the measurement ,modeling and forecasting of return volatility[R].Working paper.2005.
[27]Andersen.T G, Bollerslev.T, Diebold.F X.Roughing it up: including jumpcomponents in the measurement, modeling and forecasting of return volatility[J].Review of Economics and Statistics, 2005, 89(4),701-720.
[28]Barndorff-Nielsen O E,Shephard N.Power and bipower variation with stochasticvolatility and jumps[J]. Journal of Financial Econometrics,2004, (2):1-37.
[29]Corsi,F.,D.Pirino, and R.Ren`o.Discrete-time volatility forecasting withpersistent leverage effect and the link with continuous-time volatilitymodeling[R]. Working Paper,2010.
[30]Andersen,Bolleslev,Huang.A reduced form framework for modeling volatility ofspeculative prices based on realized variation measures[J]. Journal ofEconometrics,2011, (160):176-189.
[31]陈浪南,黄杰鲲.中国股票市场波动非对称性的实证研究[J].金融研究,2002,(5):67-73.
[32]李亚静,何跃,朱宏泉.中国股市收益率与波动性长记忆性的实证研究[J].系统工程理论与实践,2003, 1:9-15.
[33]房振明,王春峰,蒋祥林.中国股市回报波动性分析—高频数据揭示股市的特征[J].系统工程,2004, 2(22):13-19.
[34]张维,张小涛,熊熊.上海股票市场不对称研究—GJR模型与VS-GARCH模型的比较[J].数理统计与管理.2005,(11):96-102.
[35]张维,张永杰.异质信念、卖空限制与风险资产价格[J].管理科学学报,2006,(4):58-64.
[36]蒋天虹.我国股票市场波动非对称效应的反转[J].当代财经,2008, (2):65-68.
[37]陈国进,张贻军.异质信念、卖空限制与我国股市的暴跌现象研究[J].金融研究,2009, (4):80-91.
[38]黄后川,陈浪南.中国股票市场波动率的高频估计与特性分析[J].经济研究,2003, (2):74-84.
[39]徐正国,张世英.调整“已实现波动率”与GARCH及SV模型对波动的预测能力的比较研究[J].系统工程,2004,(22):60-63.
[40]徐国正,张世英.多维高频数据的“已实现”波动建模研究[J].系统工程学报，2006, 21（1）：6-11.
[41]张波,钟玉洁,田金方.基于高频数据的沪指波动的长记忆性驱动因素分析[J].统计与信息论坛,2009, 24(6):21-26.
[42]唐勇,池云果.基于已实现波动率的长记忆性分析[J].福州大学学报（哲学社会科学版）,2010, 5:27-32.
[43]曾增展.基于高频数据股票市场已实现波动率预测研究[D].中国台湾,2009.
[44]Merton R．C.On Estimating the expected return on the market：all exploratoryinvestigation[J]. Journal ofFinancial Economics,1980, 8:323-361.
[45]Engle.R F, Russell J.R.Autoregressive Conditional Duration: A New Model forIrregularly Spaced Transaction Data[J]. Econometrica, 1998, (66), 1127-1162 .
[46]Mcinish T．H．，Wood，R.A．，Intraday and overnight retums and day-of-the·weekeffect[J]. Journal of Financial Research,1985, 8:119-126.
[47]AnatR Admati，Paul Pfleiderer.A Theory of Intraday Patterns：Volume and PriceVariability[J]. The review ofFinancial Studies, 1988, l(1):3-40．.
[48]Brock W. A.,KlcidonA.W.Periodic market closure and trading volume[J].Journal of Economic Dynamic and Control, 1992, 16:451-489.
[49]Andersen, T.G.,.Return volatility and trading volume: an information flowinterpretation of stochastic volatility[J]. Journal of Finance, 1996 (51): 169-204.
[50]Andersen, T.G., Bollerslev, T,.Heterogeneous information arrivals and returnvolatility dynamics: uncovering the long-run in high frequency returns[J].Journal of Finance, 1997 (52): 975-1005.
[51]Andersen T．Q，Bollerslev T．，Cai J.Intraday and interday volatility in theJapanese stock market[J]. Journal ofIntea'national Markets, 2000,.10:107-130.
[52]Goodhart C．and Figliuoli L.Every minute counts in financial markets[J]. Journalof International Money and Finance, l991, 10:23-52.
[53]Bollerslev, Timand Domowitz.Trading Patterns and Price in the InterbankForeign Exchange Market[J]. Journal of Finance, 1993, 48:1421-1443.
[54]Stankewich,C.J.;Chapman,Jens;Muthusamy,Raman.Relationship of mechanicalfactors to the strength of proximal femur fractures fixed with cancellousscrews[J]. Journal of orthopaedic trauma,1996, 10(4):248-257.
[55]Ebens H.Realized Stock Volatility[M]. The Johns Hopkins University, 1999.
[56]唐勇.基于高频数据的金融市场分析[ D ] .天津:天津大学,2007.
[57]徐正国,张世英.高频时间序列的改进“已实现”波动特性与建模[J].系统工程学报.2005, 20(4):344-350.
[58]Andersen.T G, Bollerslev.T, Diebold.F X, Labys P.Modeling and forecastingrealized volatility[J]. Econometrica, 2003,71(2):579-625.
[59]Baillie R F, Bollerslev T, Mikkelsen H O.Fractionally integrated generalizedautoregressive conditional heteroskedasticity[J]. Journal of Econometrics,1996,74(1):3-30.
[60]Engle R. F. and T. Bollerslev.Modeling the Persistence of Conditional Variances[J]. Econometric Reviews , 1986 (5):1-50.
[61]王春峰,郑仲民,房振明.中国股市已实现“核”波动研究[J].北京理工大学学报(社会科学版),2011, 13(3):11-26.
[62]Barndorff-Nielsen O E P R Hansen A Lunde N Shephard.Designing realisedkernel to measure the ex-post variation of equity prices the presence of noise[J].Econometrica, 2008 (11):1481-1536.
[63]Barndorff-Nielsen, Peter R. Hansen, Asger Lunde and Neil Shephard.DesigningRealised Kernels to Measure the ex-post Variation of Equity Prices in thePresence of Noise,Econometrica[J]. Forthcoming,2008.
[64]汤果,何晓群,顾岚.FIGARCH模型对股市收益长记忆性的实证研究[J].统计研究,1999(7):39-42.
[65]庞淑娟,刘向丽,汪寿阳.中国期货市场高频波动率的长记忆性[J].系统工程理论与实践,2011, 6(31):1039-1044.
[66]梁丽珍,王茂斌,孔东民.交易冲击与资产的非对称波动：基于“已实现波动率”[J].金融评论.2010, (3):73-85.
[67]Calvet L. E. and A. J. Fisher.Multifractality in Asset Returns: Theory andEvidence [J]. The Review of Economics and Statistics, 2002, 84(3):381-406.
[68]LeBaron B.Stochastic volatility as a simple generator of apparent financialpower laws and long memory[J]. Quantitative Finance, 2001,1(6):621-631.
[69]张伟.基于已实现波动率的中国股票市场异质性的实证研究[D].成都：电子科技大学, 2007.
[70]Clark P K.A subordinated stochastic process model with finite variance forspeculative prices[J]. Econometrica, 1973, 41: 135-155.
[71]Zumbach, G. O. and Lynch, P.:Heterogeneous volatility cascade in financialmarkets[J]. Physica ,2001.
[72]Müller U,Dacorogna M,Dave R,Olsen R,Pictet O,Weizsacker J.Volatilities ofdifferent time resolutions-analyzing the dynamics of market components[J].Journal of Empirical Finance,1997, 4(2):213-239.
[73]文凤华,唐海如,刘晓群.中国证券市场HAR-BACD-V模型及其应用[J].系统工程理论与实践, 2012,32(3):608-613.
[74]Mandelbrot B.The Fractal Geometry of Nature[M]. W.H. Freeman andCompany,New York. 1983.
[75]Pictet O,Dacorogna M,Müller U,Olsen R,Ward J.Real-time trading models forforeign exchange rates[J]. Neural NetworkWorld,1992, 2(6):713–744.
[76]Copeland T E.A model of asset trading under the assumption of sequentialinformation arrival[J]. Journal of Finance, 1976, 31:1149-1168.
[77]Morse D.Asymmetric information in securities markets and trading volume[J].Journal of Financial and Quantitative Analysis, 1980,15:1129-1148.
[78]Karpoff. J. M.Costly Sales and the Correlation of Returns with Volume[R].Working Paper. 1985,University of WA.
[79]Robert H. Jennings, Christopher B. Barry.Information Dissemination andPortfolio Choice[J]. Journal of Financial and Quantitative Analysis,1983,18(1):1-19.
[80]Beaver,William,Lambert,Richard,Morse.The information content of securityprices[J]. Journal of Accounting and Economics, 2001, 2:-28.
[81]Epps. T. W and M. L. Epps.The Stochastic dependence of Security priceschanges and transaction volumes: implications for the mixture of distributionshypothesis[J]. Econometrica,1976, 44:305-321.
[82]Tauchen,Q. and M. Pitts.The price variability-volume relationship on thespeculative markets[J]. Econometrica,1983, 5 (1): 485-505.
[83]Harris, L.D.Conservation corridors: A highway system for wild- life. ENFOReport 85-5. Environmental Information Center of the Florida ConservationFoundation, Inc., Winter Park, FL; 1985.
[84]Torben G Andersen.Return volatility and trading volume：an information flowinterpretation of stochastic volatility[J]. Journal of finance,1996,7(1):169-204.
[85]Roman Liesenfeld.A generalized bivariate mixture model for stock pricevolatility and trading volume[J]. Journal of Econometrics, 2001,104:141-178.
[86]Lamoureux C G, Lastrapes W D.Heteroskedasticity in stock return data volumeversus GARCH effects[J]. Joural of Finance, 1990,45:221-229.
[87]Ane T, Geman N.Order flow, transaction clock and normality of asset returns[J].Journal of Finance, 2000, 55:2259-2284.
[88]吴冲锋,吴文峰.基于成交量的股价动力学分析方法[J].系统工程理论方法应用,2001, 10(1):1-7.
[89]吴冲锋,王承炜,吴文峰.交易量和交易量驱动的股价动力学分析方法[J].管理科学学报, 2002, 5(1):1-11.
[90]王承炜,吴冲锋.中国股市价格-交易量的线性及非线性因果关系研究[J].管理科学学报,2002, 5(4):7-12.
[91]李双成,邢志安,任彪.基于MDH假说的中国沪深股市量价关系实证研究[J].系统工程,2006, 24(4):77-82,
[92]耿克红,张世英.金融市场超高频时间序列ACD-GARCH-V模型研究[J].统计与决策,2007 (2):81-83,
[93]Craig A·Depken.Good Bad News and GARCH Effects in Stock Return Data[J].Journal of Applied Economics,1999, (2): 313~327.
[94]凌士勤,杨波,袁开洪.分类信息对股市波动的影响研究[J].中国管理科学,2005, 13 (3):20-25.
[95]凌士勤.异强度分类信息冲击的EGARCH效应研究[J].工业技术经济,2009,28(1):94-98.
[96]Forsberg, L., and E. Ghysels. Why do absolute returns predict volatility sowell[J]. Journal of Financial Econometrics, 2007, 5(1), 31-67
[97]刘向丽,汪寿阳,洪永淼.基于ACD模型的中国期货市场波动性分析[M].科学出版社, 2010:114-123.
[98]房振明,王春峰,蒋祥林.中国股市回报波动性分析——基于高频数据揭示股市的特征[J].系统工程,2004, 22(2):13-19.
[99]Manganelli,S.Duration, volume and volatility impact of trades[J]. Journal ofFinancial Markets, 2005,8:377-399.
[1]Andersen T G. Tim Bollerslev.Answering the Critics: Yes, ARCH Models Do Provide Good VolatilityForecasts [J]. International Economic Review, 1998(4):885-905.
[2]Koopman.S J, Jungbacker.B, Hol.E.Forecasting Daily Variability of the S&P100 Stock Index usinghistorical, realized and implied volatility measurements [J]. Journal of Empirical Finance,2005, 12(3) : 445-475.
[3]魏宇.沪深300股指期货的波动率预测模型研究[J].管理科学学报.2010,13(2):66-76.
[4]Müller U, Dacorogna M,Dave R, Pictet O,Olsen R,Ward J.Fractals and intrinsic time–A challenge toeconometricians[R]. Working paper, Olsen and Associates, 1993.
[5]Corsi F. A Simple Long memory model of realized volatility[R]. Working Paper, University ofSouthern Switzerland, 2004,http://ssrn.com/abstract=626064.
[6]Corsi, F.A simple long memory model of realized volatility[J]. Journal of Financial Econometrics,2009, 7(2), 174-196.
[7]Andersen T G. Tim Bollerslev, et.al.Exchange Rate Returns Standardized by Realized Volatility are(Nearly) Gaussian[J]. Multinational Finance Journal, 2000 ,4 :159 - 179.
[8]Andersen T G,, Tim Bollerslev T, Diebold F .The distribution of exchange rate volatility[J]. Journalof American Statistical Association, 2001,96:42-55.
[9]Andersen T. G.,Tim Bollerslev,et al.The Distribution of Stock Return Volatility [J]. Journal ofFinancial Economics，2001 ,61:43-76.
[10]Andersen.T G, Bollerslev.T, Diebold.F X, Labys P.Modeling and forecasting realized volatility[J].Econometrica, 2003,71(2):579-625.
[11]Blair BJ, Poon SH, Taylor SJ.Forcasting S&P100 Volatility:The incremental information content ofimplied volatility and high frequency index returns[J]. Journal of Econometrics,2001,45(2):195-213.
[12]Martens, M., & Zein, J.Predicting financial volatility: High-frequency time series forecasts vis-`a-vis implied volatility.[J]. Journal of Futures Markets, (2004)24, 1005–102.
[13]Koopman.S J, Jungbacker.B, Hol.E.Forecasting Daily Variability of the S&P100 Stock Index usinghistorical, realized and implied volatility measurements [J]. Journal of Empirical Finance,2005, 12(3) : 445-475.
[14]Choi K,Yu W, Zivot E.Long Memory versus Structural Breaks in Modeling and ForecastingRealized Volatility[J]. Journal of International Money and Finance,2010,54(7):117-128.
[15]Granger C.W.J.,Joyeux R.An introduction to long-memory time series models and fractionaldifferencing[J]. Journal of Time Series Analysis,1980,1(1):15-29.
[16]Hosking J.R.M.Fractional differencing[J]. Biometrika,1981,1(68):165-176.
[17]Nelson,D.B.Conditional Hetero-skedasticity in Asset Returns: A New Approach[J].Econometrica,1991, (59):347-370.
[18]Glosten,L.,Jagannathan,R.,and Runke,D.Relationship Between the Expected Value and theVolatility of the Nominal Excess Return on Stocks[J]. Journal of Finance,1993,(48):1779-1801.
[19]RabemananjaraR.and J.M.Zakoian.Threshold ARCH Model sand Asymmetries in volatility,Ch.11 inNonlinear Dynamies, Chaos and Econometries[Z]. M.H.Pesaran and S.M.Potter,NewYork:J.Wiley,1993.
[20]Baillie R F, Bollerslev T,Mikkelsen H O.Fractionally integrated generalized autoregressiveconditional heteroskedasticity[J]. Journal of Econometrics,1996, 74(1):3-30.
[21]Fornari,F.,Mele,A.Sign and volatility-switching ARCH models: theory and application tointernational stock markets[J]. Journal of Applied Econometrics, 1997.
[22]Corsi, Reno.HAR volatility modeling with heterogeneous leverage andjumps.2009.http://ssm.com/abstract=1316953.
[23]McAleer M, Medeiros MC.A multiple regime smooth transition Heterogeneous Autoregressivemodel for long memory and asymmetries[J]. Journal of Econometrics,2008, 147:104-119.
[24]Louzis, Sisinisand ,Refenes.Forecasting stock index realized volatility with an AsymmetricHAR-FIGARCH model:The case of S&P500 and DJIA stockindices.2009.http://ssrn.com/abstract=1524861
[25]Chun Liu and John M Maheu.Intraday dynamics of volatility and duration: evidence from theChinese stock market[R]. Working paper401, 2010.
[26]Andersen.T G, Bollerslev.T, Diebold.F X.Roughing it up:including jump components in themeasurement ,modeling and forecasting of return volatility[R]. Working paper.2005.
[27]Andersen.T G, Bollerslev.T, Diebold.F X.Roughing it up: including jump components in themeasurement, modeling and forecasting of return volatility[J]. Review of Economics and Statistics,2005, 89(4),701-720.
[28]Barndorff-Nielsen O E,Shephard N.Power and bipower variation with stochastic volatility andjumps[J]. Journal of Financial Econometrics,2004, (2):1-37.
[29]Corsi,F.,D.Pirino, and R.Ren`o.Discrete-time volatility forecasting with persistent leverage effectand the link with continuous-time volatility modeling[R]. Working Paper,2010.
[30]Andersen,Bolleslev,Huang.A reduced form framework for modeling volatility of speculative pricesbased on realized variation measures[J]. Journal of Econometrics,2011, (160):176-189.
[31]陈浪南,黄杰鲲.中国股票市场波动非对称性的实证研究[J].金融研究,2002, (5):67-73.
[32]李亚静,何跃,朱宏泉.中国股市收益率与波动性长记忆性的实证研究[J].系统工程理论与实践,2003, 1:9-15.
[33]房振明,王春峰,蒋祥林.中国股市回报波动性分析—高频数据揭示股市的特征[J].系统工程,2004, 2(22):13-19.
[34]张维,张小涛,熊熊.上海股票市场不对称研究—GJR模型与VS-GARCH模型的比较[J].数理统计与管理.2005,(11):96-102.
[35]张维,张永杰.异质信念、卖空限制与风险资产价格[J].管理科学学报,2006, (4):58-64.
[36]蒋天虹.我国股票市场波动非对称效应的反转[J].当代财经,2008, (2):65-68.
[37]陈国进,张贻军.异质信念、卖空限制与我国股市的暴跌现象研究[J].金融研究,2009, (4):80-91.
[38]黄后川,陈浪南.中国股票市场波动率的高频估计与特性分析[J].经济研究,2003, (2):74-84.
[39]徐正国,张世英.调整“已实现波动率”与GARCH及SV模型对波动的预测能力的比较研究[J].系统工程,2004,(22):60-63.
[40]徐国正,张世英.多维高频数据的“已实现”波动建模研究[J].系统工程学报，2006, 21（1）：6-11.
[41]张波,钟玉洁,田金方.基于高频数据的沪指波动的长记忆性驱动因素分析[J].统计与信息论坛,2009, 24(6):21-26.
[42]唐勇,池云果.基于已实现波动率的长记忆性分析[J].福州大学学报（哲学社会科学版）,2010,5:27-32.
[43]曾增展.基于高频数据股票市场已实现波动率预测研究[D].中国台湾,2009.