Copula理论及其在多变量金融时间序列分析上的应用研究
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摘要
本文主要研究Copula理论及其在多变量金融时间序列分析上的应用。论文在深入研究Copula理论的基础上，构建了基于Copula理论的多变量金融时间序列模型并系统地研究了它们的动态建模问题，最后研究了Copula模型在金融风险管理上的应用。论文的主要工作和创新点如下:
1、针对线性相关系数与传统分析方法的不足，将Copula理论引入金融分析领域。在深入探讨Copula理论的基础上，系统研究了可由Copula函数导出的非线性相关性测度和尾部相关性测度，并论述了Copula理论在金融分析上的应用。
2、相关性分析是多变量金融分析中的一个中心问题，论文在详细讨论几种重要Copula 函数在相关性分析上的应用特点的基础上，构建了基于Copula理论的多变量金融时间序列模型：Copula-GARCH和Copula-SV模型并探讨了它们的参数估计及检验问题。运用M-Copula-GARCH-t模型对上海和深圳股市之间的相关程度和相关模式进行了研究，结果表明该模型能够准确、全面地捕捉到各个时期市场间相关性的变化，正确地反映两个市场之间非对称的相关模式。
3、分析了时变相关正态Copula模型和时变相关Joe-Clayton Copula模型两种常用的时变二元Copula模型及它们相关参数的动态演进过程，对上海各板块指数收益序列的实证研究表明，时变相关二元正态Copula模型可以较好的描述对各板块间动态的相关结构，其对序列间相关关系的刻画能力和预测能力均优于静态的常相关二元正态Copula模型。
4、变结构是金融模型的基本特征，为了进一步研究金融市场之间相关结构的动态变化，提出了三类变结构Copula模型：分阶段构建的Copula模型、具有尾部变结构特性的RS-Copula模型和具有变结构边缘分布的变结构Copula模型，并研究了二元正态Copula模型变结构点的诊断方法。分别运用分阶段构建的Copula模型和RS-Copula模型对中国股市进行了研究，结果表明在刻画金融收益序列之间相关结构的能力上，变结构二元正态Copula模型优于时变相关二元正态Copula模型，RS-Copula模型优于相应的静态Copula模型。
5、金融风险管理是Copula模型的重要应用领域。论文不仅深入的研究了可用于投资组合VaR分析的Monte Carlo仿真技术，还探讨了变结构Copula模型在金融传染分析中的一些具体运用。对上海股市的实证研究表明，结合具有不同边缘分布的Copula-GARCH模型和Monte Carlo模拟法来计算资产投资组合的VaR是可行、有效的。
In this dissertation, copula theory and its applications in multivariate financial time series analysis are studied intensively. As a result of those researches, several multivariate financial time series models based on copula theory are proposed. Methods of constructing dynamic models and applications of copula models in financial risk management are also investigated systematically. The key points and main achievements of this work are listed as follows:
1. Copula theory is introduced into financial analysis to avoid defects of linear correlation coefficient and classical analysis methods. Based on fully understanding of copula theory, we investigated measure of non-linear dependence and measure of tail dependence that can be derived from copulas. Applications of copula theory in finance are also studied.
2. Dependence analysis is a central issue in multivariate financial analysis. Characters of several important copulas used in dependence analysis are discussed in this thesis and multivariate financial time series models based on copula theory, such as Copula-GARCH model and Copula-SV model, are established. Estimation and test methods of copula models are studied too. Consequentially, M-Copula-GARCH-t model is constructed and used to study the degree and patterns of dependence between Shanghai and Shenzhen stock markets. The empirical results show that strong degree and asymmetrical pattern of dependence between two markets can be described correctly and thoroughly using M-Copula-GARCH-t model.
3. Time-varying normal copula model and time-varying Joe-Clayton copula model are investigated carefully and evolution equations of their parameters are provided particularly. The empirical results from Shanghai stock market show that time-varying Copula-GARCH model is better than constant normal copula in the ability of description and prediction of dependence between financial series.
4. Structural change is a key character of financial models. In order to catch dynamic dependence between financial markets, three types of structural changing models are provided. They are staged copula model, RS-Copula model with
structural change in tail distribution and copula model with structural change in marginal distribution. At the same time, change-points detection methods of bivariate normal copula model are given in this thesis. Chinese stock markets are studied using staged copula model and RS-Copula model. The empirical results show that bivariate normal copula model with structural change is superior to time-varying bivariate copula model and RS-Copula model prevail against the static copula model in describing dependence between financial series.
5. Financial risk management is an important application area of copula technique. Not only are Monte Carlo simulation techniques which can be use to estimate portfolio Value-at-Risk investigated, but also some applications in financial contagion using structural changing copula models are discussed in this dissertation. The empirical results getting from Shanghai stock markets indicate that estimation method of portfolio Value-at-Risk, which is constructed by combining Copula-GARCH model having different marginal distributions with Monte Carlo simulation techniques, is feasible and effective.
1、针对线性相关系数与传统分析方法的不足，将Copula理论引入金融分析领域。在深入探讨Copula理论的基础上，系统研究了可由Copula函数导出的非线性相关性测度和尾部相关性测度，并论述了Copula理论在金融分析上的应用。
2、相关性分析是多变量金融分析中的一个中心问题，论文在详细讨论几种重要Copula 函数在相关性分析上的应用特点的基础上，构建了基于Copula理论的多变量金融时间序列模型：Copula-GARCH和Copula-SV模型并探讨了它们的参数估计及检验问题。运用M-Copula-GARCH-t模型对上海和深圳股市之间的相关程度和相关模式进行了研究，结果表明该模型能够准确、全面地捕捉到各个时期市场间相关性的变化，正确地反映两个市场之间非对称的相关模式。
3、分析了时变相关正态Copula模型和时变相关Joe-Clayton Copula模型两种常用的时变二元Copula模型及它们相关参数的动态演进过程，对上海各板块指数收益序列的实证研究表明，时变相关二元正态Copula模型可以较好的描述对各板块间动态的相关结构，其对序列间相关关系的刻画能力和预测能力均优于静态的常相关二元正态Copula模型。
4、变结构是金融模型的基本特征，为了进一步研究金融市场之间相关结构的动态变化，提出了三类变结构Copula模型：分阶段构建的Copula模型、具有尾部变结构特性的RS-Copula模型和具有变结构边缘分布的变结构Copula模型，并研究了二元正态Copula模型变结构点的诊断方法。分别运用分阶段构建的Copula模型和RS-Copula模型对中国股市进行了研究，结果表明在刻画金融收益序列之间相关结构的能力上，变结构二元正态Copula模型优于时变相关二元正态Copula模型，RS-Copula模型优于相应的静态Copula模型。
5、金融风险管理是Copula模型的重要应用领域。论文不仅深入的研究了可用于投资组合VaR分析的Monte Carlo仿真技术，还探讨了变结构Copula模型在金融传染分析中的一些具体运用。对上海股市的实证研究表明，结合具有不同边缘分布的Copula-GARCH模型和Monte Carlo模拟法来计算资产投资组合的VaR是可行、有效的。
In this dissertation, copula theory and its applications in multivariate financial time series analysis are studied intensively. As a result of those researches, several multivariate financial time series models based on copula theory are proposed. Methods of constructing dynamic models and applications of copula models in financial risk management are also investigated systematically. The key points and main achievements of this work are listed as follows:
1. Copula theory is introduced into financial analysis to avoid defects of linear correlation coefficient and classical analysis methods. Based on fully understanding of copula theory, we investigated measure of non-linear dependence and measure of tail dependence that can be derived from copulas. Applications of copula theory in finance are also studied.
2. Dependence analysis is a central issue in multivariate financial analysis. Characters of several important copulas used in dependence analysis are discussed in this thesis and multivariate financial time series models based on copula theory, such as Copula-GARCH model and Copula-SV model, are established. Estimation and test methods of copula models are studied too. Consequentially, M-Copula-GARCH-t model is constructed and used to study the degree and patterns of dependence between Shanghai and Shenzhen stock markets. The empirical results show that strong degree and asymmetrical pattern of dependence between two markets can be described correctly and thoroughly using M-Copula-GARCH-t model.
3. Time-varying normal copula model and time-varying Joe-Clayton copula model are investigated carefully and evolution equations of their parameters are provided particularly. The empirical results from Shanghai stock market show that time-varying Copula-GARCH model is better than constant normal copula in the ability of description and prediction of dependence between financial series.
4. Structural change is a key character of financial models. In order to catch dynamic dependence between financial markets, three types of structural changing models are provided. They are staged copula model, RS-Copula model with
structural change in tail distribution and copula model with structural change in marginal distribution. At the same time, change-points detection methods of bivariate normal copula model are given in this thesis. Chinese stock markets are studied using staged copula model and RS-Copula model. The empirical results show that bivariate normal copula model with structural change is superior to time-varying bivariate copula model and RS-Copula model prevail against the static copula model in describing dependence between financial series.
5. Financial risk management is an important application area of copula technique. Not only are Monte Carlo simulation techniques which can be use to estimate portfolio Value-at-Risk investigated, but also some applications in financial contagion using structural changing copula models are discussed in this dissertation. The empirical results getting from Shanghai stock markets indicate that estimation method of portfolio Value-at-Risk, which is constructed by combining Copula-GARCH model having different marginal distributions with Monte Carlo simulation techniques, is feasible and effective.
引文
洪永淼.金融计量的新近发展[J].经济学(季刊),2002,1(2):249-268.
Engle R F. Autoregressive heteroskedasticity with estimation of the variance of U.K. inflation[J]. Econometrica, 1982, 50: 987-1008.
Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Economics, 1986, 31: 307-327.
吴长凤.利用回归—GARCH模型对我国沪深股市的分析[J].预测,1999,4:46-47.
王军波,邓述慧.利率、成交量对股价波动的影响——GARCH修正模型的应用[J].系统工程理论与实践,1999,(9):49-57.
叶阿忠,李子奈.我国通货膨胀的GARCH模型[J].系统工程理论与实践,2000,(10):46-48.
朱世武,应惟伟.国债发行规模的实证研究[J].金融研究,2000,(11):49-57.
叶青.基于GARCH和半参数法的VaR模型及其在中国股市风险分析中的应用[J].统计研究,2000,(12):25-29.
Engle R F, Bollerslev T. Modeling the persistence of conditional variances[J]. Econometric Review, 1986, 5: 1-50.
Nelson D B. Conditional heteroskedasticity in asset returns: A new approach[J]. Econometrica, 1991, 59: 347-370.
Baillie R T, Bollerslev T, Mikkelsen H O. Fractionally integrated generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1996, 74: 3-30.
张世英,柯珂. ARCH模型体系[J].系统工程学报,2002,17(3):236-245.
Hamilton J D, Susmel R. Autoregressive conditional heteroskedasticity and changes in regime[J]. Journal of Econometrics, 1994(64):307-333.
Hamilton J D. A new approach to the economic analysis of nonstationary time series and the business cycle [J]. Econometrica, 1989(57):358-384.
Bollerslev T. On the correlation structure for the generalized autoregressive conditional heteroskedastic process[J]. Journal of Time Series Analysis, 1988, 9: 121-131.
Engle R F, Kroner K F. Multivariate simultaneous generalized ARCH[J].
Econometric Theory, 1995, 11: 122-150.
Bollerslev T. Modeling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model[J]. Review of Economics and Statistics, 1990,72: 498-505.
Engle R F. Dynamic conditional correlation — A simple class of multivariate GARCH models. NBRE working paper, 2002.
Billio M, Pelizzon L. Value-at-Risk a multivariate switching regime approach[J]. Journal of Empirical Finance, 2000,7:531-554.
Vlaar P J G. Value at risk models for Dutch bond portfolios[J]. Journal of Banking and Finance, 2000,24:1131-1154.
Wang C F, Li G. Improving the estimation of VaR-GARCH using genetic algorithm[J]. Journal of Systems Science and Systems Engineering, 2001, 10(3):281-290.
Hsieh D. Implication of nonlinear dynamics for financial risk management[J]. Journal of Financial and Quantitative Analysis,1993,28(1):41-64.
Beltratti A, Morana C. Computing value at risk with high frequency data[J]. Journal of Empirical Finance, 1999,6:431-455.
Clark P K. A subordinated stochastic process model with finite variance for speculative prices[J]. Econometrica, 1973, 41: 135-155.
Tauchen G, Pitts M. The price variability-volume relationship on speculative market[J]. Econometrica, 1983, 51: 485-505.
Taylor S J. Modeling financial time series [M]. New York: Wiley, 1986.
Liesenfeld R, Jung R C. Stochastic volatility models: conditional normality versus heavy-tailed distributions[J]. Journal of Applied Econometrics, 2000, 15: 137-160.
Breidt F J, et al. The detection and estimation of long memory in stochastic volatility [J]. Journal of Econometrics, 1998,83: 325-348.
Harvey A, Shephard N. Estimation of an asymmetric stochastic volatility model for asset returns [J]. Journal of Business & Economic Statistics, 1996,14: 429-434.
So M K P, Lam K, Li W K. A stochastic volatility model with Markov-switching, Journal of Business[J]. Economic Statistics, 1998, 16: 244-253.
Smith D R. Markov-switching stochastic volatility diffusion models of short
term interest rates[D].2000.
Harvey A, Ruiz E, Shephard N. Multivariate stochastic variance models[J]. Review of Economic Studies. 1994,61: 247-264.
So M K P, Lam K. Multivariate modeling of the autoregressive random variance process[J]. Journal of Time Series Analysis, 1997,18: 429-446.
Ceske R, Hernandez J. Where theory meets practice. Risk Magazine (Operational Risk Report). 1999,12:17-20.
Embrechts P A, McNeil A, Straumann D. Correlation: Pitfalls and Alternatives[J].RISK.1999,12 (5), 11-21.
Li D X. On default correlation: a copula function approach. Journal of Fixed Income, 2000, (3): 43 - 54.
Nelsen R B. An introduction to copulas[M]. New York: Springer, 1998.
Bouyé E, Durrleman V, Nikeghbali A, et al. Copula: an open fields for risk management. Working Paper of Financial Econometrics Research Centre, City University Business School, London, 2001.
Alexander C O. Volatility and correlation: methods, models and applications. Risk Management and Analysis: Measuring and Modeling Financial Risk(C.O. Alexander, Ed.) Wiley.
Hamao,Y. and R.W. Masulis, and V.K.Ng. Correlation in Price Changes and Volatility across International Stock Markets[J]. Review of Financial Studies, 1990,2(3):281-307.
Sola M, Spagnolo F, Spagnolo N. A test for volatility spillovers[J]. Economics Letters. 2002,76:77-84.
Susmel R, Engle R F. Hourly Volatility Spillovers Between International Equity Markets[J]. Journal of International Money and Finance, 1994,13(1):3-25.
史道济.相关系数与相关性[J].统计科学与实践,2002,(4):22-24
朱宏泉,卢祖帝,汪寿阳.中国股市的Granger因果关系分析[J].管理科学学报,2001,4(5):7-12.
Boyer B H, Gibson M S, Loretan M. Pitfalls in tests for changes in correlation. International Finance Discussion Paper No.597. 1999.
张尧庭. 我们应该选用什么样的相关性指标？[J]. 统计研究，2002, (9):41-44.
Nelsen R B. Dependence and order in families of Archimedean Copulas[J]. Journal of Multivariate Analysis. 1997,60: 111-122.
Wei, G, Hu T Z. Supermodular dependence ordering on a class of multivariate copulas[J]. Statistics and Probability Letters. 2002,57(4): 375-385 .
Vandenhende F, Lambert P. Improved rank-based dependence measures for categorical data[J]. Statistics and Probability Letters. 2003,63(2):157-163 .
Kowalezyk T. Link between grade measures of dependence and of separability in pairs of conditional distribution[J]. Statistics & Probability Letters. 2000,46:371-379.
Patton A J. Skewness, Asymmetric Dependence, and Portfolios. Working paper of London School of Economics & Political Science, 2002.
Cuculescu Ioan, Theodorescu Radu. Extreme value attractors for star unimodal copulas[J]. Comptes Rendus Mathematique .2002, 334(8): 689-692.
Hürlimann Werner. Hutchinson-Lai's conjecture for bivariate extreme value copulas[J]. Statistics and Probability Letters. 2003, 61(2):191-198.
Sklar A. Fonctions de repartition à n dimensions et leurs marges[J]. Publication de l'Institut de Statistique de l'Université de Paris, 1959,8:229-231.
Nelsen R B, Quesada-Molina J J, Rodríguez-Lallena J A, et. al. Distribution functions of copulas: a class of bivariate probability integral transforms[J]. Statistics and Probability Letters 2001,54(3): 277-282.
Genest C, Rivest L P. On the multivariate probability integral transformation[J]. Statistics and Probability Letters. 2001,53(4):391-399.
Rodríguez-Lallena José A, úbeda-Flores Manuel. Distribution functions of multivariate copulas[J]. Statistics and Probability Letters. 2003, 64(1):41-50.
Tibiletti L. Beneficial Changes in Random Variables via Copulas: An Application to Insurance[J]. Insurance: Mathematics and Economics. 1997,19(2):166.
Shemyakin A, Youn H. Bayesian estimation of joint survival functions in life insurance. Working Paper of University of St. Thomas, Saint Paul, MN, USA. 2002.
Frahm G, Junker M, Szimayer A. Elliptical copulas: applicability and limitations[J]. Statistics and Probability Letters. 2003,63(3):275-286.
Cossette H, Gaillardetz P, Marceau é, et al. On two dependent individual risk models[J]. Insurance: Mathematics and Economics. 2002, 30(2):153-166.
Meade Nigel, Islam Towhidul. Modelling the dependence between the times to international adoption of two related technologies[J]. Technological Forecasting
and Social Change. 2003,70(8): 759-778.
Vaz de Melo Mendes Beatriz, Martins de Souza Rafael. Measuring financial risks with copulas[J]. International Review of Financial Analysis. 2004 13: 27-45 .
Bollerslev T, Engle R F, Wooldridge J M. A Capital Asset Pricing Model with Time Varying Covariances[J]. Journal of Political Economy. 1988,96: 116-131.
Kroner K F, Claessens S. Optimal Dynamic Hedging Portfolios and the Currency Composition of External Debt[J]. Journal of International Money and Finance, 1991,10:131-148.
Engle R F, Joseph M. GARCH for Groups[J]. Risk. 1996, 9(8): pp 36-40.
Ding Zh X, Engle R F.Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing. Academia Economic Papers, 2001,29(2):157-184.
Longin F, Solnik B. Is the correlation in international equity return constant: 1960-1990?[J]. Journal of International Money and Finance.1995,14(1):3-26.
Longin F, Solnik B. Extreme Correlation of International Equity Markets[J]. Journal of Finance, 2001,56(2):649-676.
孙炳堃,史道济.二元Cauchy分布尾部的相关性[J].天津大学学报,2000,33(4):432-434.
Hu L. Essays in econometrics with applications in macroeconomic and financial modelling[D]. New Haven: Yale University, 2002.
Joe H. Multivariate Models and Dependence Concepts[M]. London: Chapman & Hall, 1997.
Frees E W, Valdez E A. Understanding Relationships using Copulas[J]. North American actuarial journal, 1998,2 (1): 1-25.
Schmitz, V. Revealing the dependence structure between X(1) and X(n)[J]. Journal of Statistical Planning and Inference. 2004,123(1): 41-47.
Rockinger M, Jondeau E. Conditional dependency of financial series: an application of copulas. Working Paper of Department of Finance, HEC School of Management, Paris, 2001.
Patton A J. Modeling time-varying exchange rate dependence using the conditional copula. Working Paper of Department of Economics, University of California, San Diego, 2001.
Patton A J. Estimation of copula models for time series of possibly different lengths. Working Paper of Department of Economics, University of California,
San Diego, 2001.
Rodriguez J C. Measuring financial contagion: a copula approach. Working Paper of European Institute for Statistics, Probability, Operation Research and their Applications.2003.
朱国庆.金融机构风险测量方法研究[博士学位论文].天津:天津大学,2000.
张尧庭.连接函数（Copula）技术与金融风险分析[J].统计研究,2002, (4):48-51.
史道济,关静. 沪深股市风险的相关性分析[J].统计研究,2003,(10):45-48.
杜本峰,郭兴义.一种新的风险度量工具:PaV及其计算框架[J].统计研究,2003, (2):48-50.
韦艳华,张世英,孟利锋.Copula技术及其在金融时间序列分析上的应用[J].系统工程,2003,21(增刊):41-45.
韦艳华,张世英,孟利锋.Copula理论在金融上的应用[J].西北农林科技大学学报(社会科学版),2003,3(5):97-101.
韦艳华,张世英.金融市场的相关性分析—Copula-GARCH模型及其应用[J].系统工程,2004,22(4):7-12.
韦艳华,张世英,郭焱.金融市场相关程度与相关模式的研究[J].系统工程学报,2004,19(4):355-362.
Patton A J. On the out-of-sample importance of skewness and asymmetric dependence for asset allocation. Working Paper of Department of Economics, University of California, San Diego, 2001.
Bouyé E, Durrleman V, Nikeghbali A, et al. Copulas for finance: a reading guide and some applications. Working Paper of Financial Econometrics Research Centre, City University Business School, London, 2000.
Fisher R A. Statistical Methods for Research Workers[M].1932.
Casella G, Berger R L. Statistical Inference[M]. Duxbury Press, U.S.A.,1990.
Genest C, Mackay J. The joy of Copulas: Bivariate distributions with uniform marginals[J]. American Statistician. 1986,40:280-283.
Genest C. Frank's family of bivariate distributions[J]. Biometrika. 1987,74:549-555.
Genest C, Rivest L P. Statistical inference procedures for bivariate Archimedean copulas[J]. Journal of the American Statistical Association. 1993,88:1034-1043.
Genest C, Ghoudi K, Rivest L P. Discussion of "Understanding relationships
using copulas, by Edward Frees and Emiliano Valdez"[J]. North American Actuarial Journal. 1998,3:143-149.
Schwettzer B, Wolff E. On nonparametric measures of dependence for random variables[J]. Annals of Statistics. 1981,9:879-885.
Coles S, Currie J, Tawn J. Dependence measures for extreme value analyses. Working Paper of Department of Mathematics and Statistics, Lancaster University. 1999.
Juri A. Tail dependence from a distributional point of view. Working paper of Eidgen?ssische Technische Hochschule Zürich Swlss Federal Institute of Technology Zurich, 2002.
Juri A, Wütrich M V. Copula Convergence Theorems for Tail Events[J]. Insurance: Mathematics and Economics, 2002,30:405-420.
Rosenberg J V. Nonparametric pricing of multivariate contingent claim. Working paper of Stern School of Business, New York University. 2000.
Hull J, White A. Value at Risk when daily changes in market variables are nor normally distributed[J]. Journal of Derivatives. 1998,5(3):9-19.
Bouyé E, Ganssel N, Salmon. Investigating Dynamic Dependence Using Copulae. Working Paper of Financial Econometrics Research Centre, City University Business School, London, 2002.
Li W K, Mak T K. On the squared residual autocorrelations in non-linear time series with conditional heteroscedasticity[J]. Journal of Time Series Analysis. 1994,15: 627-636.
Engle R F, Ito T, Lin W L. Meteor showers or heat waves?[J]. Heteroskedastic intra-daily volatility in the foreign exchange market. Econometrica. 1993,58: 525-542.
Karolyi G A. A multivariate GARCH model of international transmissions if stock returns and volatility: the case of the United States and Canada[J]. Journal of Business and Economic Statistics. 1995,13: 11-25.
Jeong J G. Cross-border transmission of stock price volatility: evidence from the overlapping trading hours[J]. Global Finance Journal. 1999,10:53-70.
Brooks C, Henry O T. Linear and non-linear transmission of equity return volatility : evidence from the US，Japan and Australia. Economic Modeling[J]. 2000,17:497-513.
Longin F, Solnik B. Extreme correlation of international equity markets[J].
Journal of Finance, 2001.649-676.
Ramchmand L, Susmel R. Volatility and cross correlation across major stock markets[J]. Journal of Empirical Finance. 1998,5: 397-416.
Ito T, Lin W L. Price volatility and volume spillovers between the Tokyo and New York stock markets. Working Paper of NBER .1994.
Lin W L, Engle R F, Ito T. Do bulls and bears move across borders? International transmission of stock returns and volatility[J]. The Review of Financial Studies. 1994,63: 383-538.
Campbell J Y, Ammer J. What moves the stock and bond markets? A variance decomposition for long-term asset returns[J]. Journal of Finance, 1993,48: 3-37.
Shiller R J, Beltratti A E. Stock prices and bond yields –Can their comovements be explained in terms of present value model?[J]. Journal of Monetary Economics. 1992,30: 25-46.
Cebrian A C, Denuit M, Scaillet O. Testing for Concordance Ordering. Working Paper of University of Zaragoza - General, Catholic University of Louvain (UCL) - General and HEC Geneve UNI MAIL .2002
Denuit M, Scaillet O. Nonparametric Tests for Positive Quadrant Dependence. Working Paper of Catholic University of Louvain (UCL) - General and HEC Geneve UNI MAIL. 2002.
Das S R, Geng G. Correlated Default Processes: A Criterion-Based Copula Approach. Working Paper of Leavey School of Business, Santa Clara University .2004.
Yu F. Dependent Default in Intensity-Based Models. Working Paper of University of California, Irvine - Finance Area. 2003.
Junker M, Szimayer A, Wagner N. Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications. Working Paper of Financial Engineering Group, Center of Advanced European Studies and Research, Germany (CAESAR). 2003.
Chen X H, Fan Y Q, Patton A J. Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates. Working Paper of Department of Economics, New York University. 2004.
Rosenberg J V, Schuermann T. A General Approach to Integrated Risk Management with Skewed, Fat-Tailed Risk. Working Paper of Research and
Market Analysis Group, Federal Reserve Bank of New York .2004.
Granger C W J, Terasvirta T, Patton A J. Common Factors in Conditional Distributions for Bivariate Time Series. Working Paper of University of California, San Diego - Department of Economics, 2004.
Quintos C . Estimating Tail Dependence and Testing for Contagion Using Tail Indices. Working Paper of University of Rochester - William E. Simon Graduate School of Business Administration. 2001.
Wise M B, Bhansali V. Implications of Correlated Default for Portfolio Allocation to Corporate Bonds. Working Paper of California Institute of Technology - General and Pacific Investment Management Company (PIMCO) - General, 2002.
Malevergne Y, Sornette D. Testing the Gaussian Copula Hypothesis for Financial Assets Dependences. Working Paper of University of Nice and UCLA and LPMC. 2001.
Schonbucher P, Schubert D. Copula-Dependent Defaults in Intensity Models. Working Paper of Department of Mathematics and KPMG, Swiss Federal Institute of Technology Zurich. 2002.
Jondeau E, Rockinger M. Conditional Dependency of Financial Series: The Copula-GARCH Model. Working Paper of Economic Study and Research Division, Banque de France. 2003.
Dhaene J, Denuit M, Goovaerts M, et al. The Concept of Comonotonicity in Actuarial Science and Finance: Theory. Working Paper of Department of Applied Economics, Katholieke Universiteit Leuven (KUL). 2003.
Mandelbrot B. The Variation of certain speculative prices[J]. Journal of Business. 1963,36:394-419.
Fama E F. The behavior of stock market prices[J]. Journal of Business. 1965, 38: 34-105
李汉东.多变量时间序列持续性研究[博士学位论文].天津:天津大学,2000.
柯珂.ARCH模型族的建模研究[硕士学位论文].天津:天津大学, 2000.
柯珂,张世英.ARCH模型的诊断分析[J].管理科学学报,2001,4(2):12-18.
杜子平.基于波动模型的金融市场分析[博士学位论文].天津:天津大学,2002.
Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility models［J］. Journal of Business & Economic Statistics. 1994, 12: 371-388.
Hull J, White A. The pricing of options on assets with stochastic volatilities[J].
The Journal of Finance. 1987, XLII(2): 281-299.
Melino A, Turnbull S M. Pricing foreign currency options with stochastic volatility[J]. Journal of Econometrics. 1990, 45: 239-265.
Harvey A C. Long memory in stochastic volatility. Working Paper of London School of Economics.1993.
Kim S, Shephard N, Chib S. Stochastic volatility: likelihood inference and comparison with ARCH models[J]. Review of Economic Studies. 1998,65: 361-393.
Board J L G, Sandmann G, Sutcliffe C M S. The effect of contemporaneous futures market volume on spot market volatility. Working Paper of London School of Econometrics. 1997.
Ghysels E, Goureroux C, Jasiak J. Stochastic volatility and time deformation: an application to trading volume and leverage effects. Working Paper of Univerite de Montreal. 1996.
Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility models with fat-tail and correlated errors[J]. Journal of Business & Economic Statistics. 1994, 12: 371-388.
Ruiz E. Quasi-maximum likelihood estimation of stochastic volatility models[J]. Journal of Econometrics. 1994, 63: 289-306.
Watanabe T. A non-linear filtering approach to stochastic volatility models with an application to daily stock returns[J]. Journal of Applied Econometrics. 1999, 14: 101-121.
Danielsson J. Stochastic volatility in asset prices: estimation with simulated maximum likelihood[J]. Journal of Econometrics. 1994, 61: 375-400.
Danielsson J, Richard J F. Accelerated Gaussian importance sampler with application to dynamic latent variable models, Journal of Applied Econometrics[J]. 1993, 8: 153-173.
Andersen T. Chung H, Sorensen B. Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study[J]. Journal of Econometrics. 1999,91:61-87.
Meyer R, Yu J. Bugs for a Bayesian analysis of stochastic volatility models[J]. Econometrics Journal. 2000,3:198-215.
Yu J. MCMC methods for estimating stochastic volatility models with leverage effect: comments on Jacquier, Polson and Rossi. Working Paper of Department
of Economics, University of Auckland, New Zealand.2002.
Hennessy D, Lapan H E. The Use of Archimedean Copulas to Model Portfolio Allocations[J]. Mathematical Finance. 2002, 12: 143-154.
Smith M. Modeling Sample Selection Using Archimedean Copulas[J]. Econometrics Journa.2003, 6: 99-123.
Taylor S J, Wang Y H. Option Prices and Risk-Neutral Densities for Currency Cross-Rates. Working Paper of Department of Accounting and Finance, Lancaster University .2004.
Valdez E A. Bivariate ananlysis of survivorship and persistency[J]. Insurance: Mathematics and Economics. 2001,29:357-373.
Xu Y. Modelling dependence between financial returns with copulas and stochastic volatility marginal. Working Paper of Department of Economics, University of Miami. 2003.
Anderson T W. Maximum likelihood estimates for a multivariate Normal distribution when some observations are missing[J]. Journal of the American Statistical Association. 1957,52:200-203.
Little R J A, George C. Theory of point estimation[M]. New York: Springer, 1998.
Stambaugh R F. Analyzing investments whose histories differ in length[J]. Journal of Financial Economics, 1997,45:285-331.
Diebold F X, Gunther T, Tay A S. Evaluating density forecasts with applications to financial risk management[J]. International Economic Review, 1998,39:863-883.
Diebold F X, Hahn J, Tay A S. Multivariate density forecast evaluation and calibration in financial risk management: high-frequency returns on foreign exchange[J]. The Review of Economics and Statistics, 1999,81(4):661-673.
Shao J. Mathematical statistics[M].New York: Springer, 1999.
吴喜之,王兆军.非参数统计方法[M].北京:高等教育出版社,1996.
Klugman S A, Parsa R. Fitting bivariate loss distributions with copulas[J]. Insurance: Mathematics and Economics. 1999,24(1-2): 139-148.
Christoffersen P F. Evaluating interval forecasts[J]. International Economic Review, 1998,39(4):841-862.
Engel R B, Manganelli S. CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles. Working Paper of Department of Economics,
University of California, San Diego.1999.
Goorbergh R W J, Genest C, Werker B J M. Multivariate option pricing using dynamic copula models. Working Paper of Department of Finance and Center for Economic Research, Tilburg University. 2003.
Bollerslev T, Mikkelsen H O. Modeling and pricing long memory in stock market volatility[J]. Journal of Econometrics, 1996,73:151-184.
Ding Z, Granger C W J, Engle R F. A long memory property of stock market returns and a new model[J]. Journal of Empirical Finance, 1993,1:83-106.
苏卫东,张世英.随机波动模型分析及其在上海股市的应用[J]. 系统工程理论方法应用,2001,10(3):202-206.
Lamoureux C G, Lastrapes W D. Persistence in variance, structural change, and the GARCH model[J]. Journal of Business & Economic Statistic, 1990,8:225-234.
苏卫东.金融波动模型及其在中国股市的应用[博士学位论文].天津:天津大学,2002
苏卫东,张世英. 变截距SV模型及其在上海股市的实证. 系统工程理论方法应用, 2002,12(3):57-63
孙青华. 长记忆向量时间序列协整建模理论与变结构研究[博士学位论文]. 天津: 天津大学,1999.
孙金丽. 变结构波动建模及其应用[硕士学位论文]. 天津: 天津大学,2003.
白崑. 随机波动模型及其应用[硕士学位论文]. 天津: 天津大学,2002.
郭名媛. 具有马尔可夫结构转换机制的波动模型及其应用[硕士学位论文]. 天津: 天津大学,2003.
徐梅. 金融波动分析的小波和频域方法研究[博士学位论文]. 天津: 天津大学,2003.
Dueker. Markov switching in GARCH processes and mean reverting stock market volatility[J]. Journal of Business and Economic Statistics , 1997(1):45-69.
Cai. A Markov model of switching-regime ARCH[J]. Journal of Business and Economic Statistics, 1994(12):309-316.
Kalimipalli, Susmel. Regime-switching stochastic volatility and short-term interest rates. Working Papers.2002.
Forbes K, Rigobon R. No contagion, only interdependence: measuring stock markets comovements[J]. Journal of Finance, 2002,57(5):2223-2261.
Baig T, Goldfaijn I. Financial market contagion in the Asian crisis. Working Paper of IMF Staff. 1998.
Ellis L, Lewis E. The response of financial markets in Australia and New Zealand to News about the Asian crisis. BIS Conference on International Financial Markets and Implications for Monetary and Financial Stability, Basle. 1999,8:25-26.
Dungey M, Zhumabekova D, Scholar V. Testing for contagion using correlations: some words of caution. Working Paper of Pacific Basin, 2001.
Pedhazur E J. Multiple regression in behavioral research[M]. Orlando: Harcourt Brace College Publishers, 1997.
黄违洪,张世英.模型结构变化点检测法[J]. 应用数学学报, 1987, 10(3):267-275.
Kim D. A Bayesian significance test on the stationarity of regression parameters[J]. Biometrika, 1991,78:667-675.
Kim D, Kon S J. Structural change and time dependence in models of stock returns[J]. Journal of Empirical Finance, 1999, (9):283-308.
Lindley D V. Introduction to Probability and Statistics from a Bayesian Viewpoint. Vol. 2.Cambridge University Press, Cambridge.1965.
Box G E P, Tiao G C. Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, MA. 1973.
Cherubini U, Luciano E. Value-At-Risk Trade-Off and Capital Allocation with Copulas. Working Paper of Department of Statistics and Applied Mathematics, Polyhedron Computational Finance and University of Turin. 2001.
Schonbucher P. Taken to the Limit: Simple and Not-So-Simple Loan Loss Distributions Working Paper of Department of Mathematics, Swiss Federal Institute of Technology Zurich. 2003.
Tibiletti L. The Riskier the Assets, the Riskier the Portfolios: Pitfalls and Misinterpretations. Working Paper of Department of Statistics and Applied Mathematics, University of Turin. 2003.
Glasserman P, Heidelberger P, Shahabuddin P. Portfolio Value-at-Risk with Heavy-Tailed Risk Factors. Working Paper of Graduate School of Business, Columbia University, New York.2000.
Frey R. Dependent Defaults in Models of Portfolio Credit Risk. Working Paper of Department of Mathematics, University of Leipzig. 2003.
Embrechts P A, McNeil A, Straumann D. Correlation and Dependence in Risk Management: Properties and Pitfalls. Working Paper.1999.
Clemente A D, Romano C. Measuring portfolio Value-at-Risk by a copula-EVT based approach. Working Paper of University of Rome "La Sapienza", 2003.
Rosenberg J, Schuermann T. A General Approach to Integrated Risk Management with Skewed, Fat-tailed Risks. Working Paper of Federal Reserve Bank of New York, 2004.
Rank J, Siegl T. Applications of copulas for the calculation of Vaule-at-Risk. Working Paper. 2003.
Romano C. Applying copula function to risk mangement. Working Paper of University of Rome "La Sapienza", 2002
Devroye. Non-uniform random variate generation[M]. New York: Springer-Verlag, 1986.
Bertero E, Colin M. Structure and Performance: Global Interdependence of Stock Markets Around the Crash of October 1987. Working Paper of C.E.P.R. 1989.
King M, Wadhwani S. Transmission of Volatility Between Stock Markets. Review of Financial Studies.1990.
Calvo S, Reinhart C. Capital Flows to Latin America: Is There Evidence of Contagion Effects? Working Paper.1996.
Longin F, Solnik B. Is the Correlation in International Equity Returns Constant: 1960-1990?[J]. Journal of International Money and Finance. 1995,14: 3-26.
Hartman P, Straetmans S, de Vries C. Asset market linkages in crisis periods. Working Paper of Erasmus, 2000.
Ang A, Bekaert G. International Asset Allocation with Regime Shifts[J]. Review of Financial Studies. 2002,15(4):1137-1187.
Chesney F, Jondeau E. Does Correlation Between Stock Returns Really Increase During Turbulent Period? Working Paper of Banque de France, 2000.
Engle R F. Autoregressive heteroskedasticity with estimation of the variance of U.K. inflation[J]. Econometrica, 1982, 50: 987-1008.
Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Economics, 1986, 31: 307-327.
吴长凤.利用回归—GARCH模型对我国沪深股市的分析[J].预测,1999,4:46-47.
王军波,邓述慧.利率、成交量对股价波动的影响——GARCH修正模型的应用[J].系统工程理论与实践,1999,(9):49-57.
叶阿忠,李子奈.我国通货膨胀的GARCH模型[J].系统工程理论与实践,2000,(10):46-48.
朱世武,应惟伟.国债发行规模的实证研究[J].金融研究,2000,(11):49-57.
叶青.基于GARCH和半参数法的VaR模型及其在中国股市风险分析中的应用[J].统计研究,2000,(12):25-29.
Engle R F, Bollerslev T. Modeling the persistence of conditional variances[J]. Econometric Review, 1986, 5: 1-50.
Nelson D B. Conditional heteroskedasticity in asset returns: A new approach[J]. Econometrica, 1991, 59: 347-370.
Baillie R T, Bollerslev T, Mikkelsen H O. Fractionally integrated generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1996, 74: 3-30.
张世英,柯珂. ARCH模型体系[J].系统工程学报,2002,17(3):236-245.
Hamilton J D, Susmel R. Autoregressive conditional heteroskedasticity and changes in regime[J]. Journal of Econometrics, 1994(64):307-333.
Hamilton J D. A new approach to the economic analysis of nonstationary time series and the business cycle [J]. Econometrica, 1989(57):358-384.
Bollerslev T. On the correlation structure for the generalized autoregressive conditional heteroskedastic process[J]. Journal of Time Series Analysis, 1988, 9: 121-131.
Engle R F, Kroner K F. Multivariate simultaneous generalized ARCH[J].
Econometric Theory, 1995, 11: 122-150.
Bollerslev T. Modeling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model[J]. Review of Economics and Statistics, 1990,72: 498-505.
Engle R F. Dynamic conditional correlation — A simple class of multivariate GARCH models. NBRE working paper, 2002.
Billio M, Pelizzon L. Value-at-Risk a multivariate switching regime approach[J]. Journal of Empirical Finance, 2000,7:531-554.
Vlaar P J G. Value at risk models for Dutch bond portfolios[J]. Journal of Banking and Finance, 2000,24:1131-1154.
Wang C F, Li G. Improving the estimation of VaR-GARCH using genetic algorithm[J]. Journal of Systems Science and Systems Engineering, 2001, 10(3):281-290.
Hsieh D. Implication of nonlinear dynamics for financial risk management[J]. Journal of Financial and Quantitative Analysis,1993,28(1):41-64.
Beltratti A, Morana C. Computing value at risk with high frequency data[J]. Journal of Empirical Finance, 1999,6:431-455.
Clark P K. A subordinated stochastic process model with finite variance for speculative prices[J]. Econometrica, 1973, 41: 135-155.
Tauchen G, Pitts M. The price variability-volume relationship on speculative market[J]. Econometrica, 1983, 51: 485-505.
Taylor S J. Modeling financial time series [M]. New York: Wiley, 1986.
Liesenfeld R, Jung R C. Stochastic volatility models: conditional normality versus heavy-tailed distributions[J]. Journal of Applied Econometrics, 2000, 15: 137-160.
Breidt F J, et al. The detection and estimation of long memory in stochastic volatility [J]. Journal of Econometrics, 1998,83: 325-348.
Harvey A, Shephard N. Estimation of an asymmetric stochastic volatility model for asset returns [J]. Journal of Business & Economic Statistics, 1996,14: 429-434.
So M K P, Lam K, Li W K. A stochastic volatility model with Markov-switching, Journal of Business[J]. Economic Statistics, 1998, 16: 244-253.
Smith D R. Markov-switching stochastic volatility diffusion models of short
term interest rates[D].2000.
Harvey A, Ruiz E, Shephard N. Multivariate stochastic variance models[J]. Review of Economic Studies. 1994,61: 247-264.
So M K P, Lam K. Multivariate modeling of the autoregressive random variance process[J]. Journal of Time Series Analysis, 1997,18: 429-446.
Ceske R, Hernandez J. Where theory meets practice. Risk Magazine (Operational Risk Report). 1999,12:17-20.
Embrechts P A, McNeil A, Straumann D. Correlation: Pitfalls and Alternatives[J].RISK.1999,12 (5), 11-21.
Li D X. On default correlation: a copula function approach. Journal of Fixed Income, 2000, (3): 43 - 54.
Nelsen R B. An introduction to copulas[M]. New York: Springer, 1998.
Bouyé E, Durrleman V, Nikeghbali A, et al. Copula: an open fields for risk management. Working Paper of Financial Econometrics Research Centre, City University Business School, London, 2001.
Alexander C O. Volatility and correlation: methods, models and applications. Risk Management and Analysis: Measuring and Modeling Financial Risk(C.O. Alexander, Ed.) Wiley.
Hamao,Y. and R.W. Masulis, and V.K.Ng. Correlation in Price Changes and Volatility across International Stock Markets[J]. Review of Financial Studies, 1990,2(3):281-307.
Sola M, Spagnolo F, Spagnolo N. A test for volatility spillovers[J]. Economics Letters. 2002,76:77-84.
Susmel R, Engle R F. Hourly Volatility Spillovers Between International Equity Markets[J]. Journal of International Money and Finance, 1994,13(1):3-25.
史道济.相关系数与相关性[J].统计科学与实践,2002,(4):22-24
朱宏泉,卢祖帝,汪寿阳.中国股市的Granger因果关系分析[J].管理科学学报,2001,4(5):7-12.
Boyer B H, Gibson M S, Loretan M. Pitfalls in tests for changes in correlation. International Finance Discussion Paper No.597. 1999.
张尧庭. 我们应该选用什么样的相关性指标？[J]. 统计研究，2002, (9):41-44.
Nelsen R B. Dependence and order in families of Archimedean Copulas[J]. Journal of Multivariate Analysis. 1997,60: 111-122.
Wei, G, Hu T Z. Supermodular dependence ordering on a class of multivariate copulas[J]. Statistics and Probability Letters. 2002,57(4): 375-385 .
Vandenhende F, Lambert P. Improved rank-based dependence measures for categorical data[J]. Statistics and Probability Letters. 2003,63(2):157-163 .
Kowalezyk T. Link between grade measures of dependence and of separability in pairs of conditional distribution[J]. Statistics & Probability Letters. 2000,46:371-379.
Patton A J. Skewness, Asymmetric Dependence, and Portfolios. Working paper of London School of Economics & Political Science, 2002.
Cuculescu Ioan, Theodorescu Radu. Extreme value attractors for star unimodal copulas[J]. Comptes Rendus Mathematique .2002, 334(8): 689-692.
Hürlimann Werner. Hutchinson-Lai's conjecture for bivariate extreme value copulas[J]. Statistics and Probability Letters. 2003, 61(2):191-198.
Sklar A. Fonctions de repartition à n dimensions et leurs marges[J]. Publication de l'Institut de Statistique de l'Université de Paris, 1959,8:229-231.
Nelsen R B, Quesada-Molina J J, Rodríguez-Lallena J A, et. al. Distribution functions of copulas: a class of bivariate probability integral transforms[J]. Statistics and Probability Letters 2001,54(3): 277-282.
Genest C, Rivest L P. On the multivariate probability integral transformation[J]. Statistics and Probability Letters. 2001,53(4):391-399.
Rodríguez-Lallena José A, úbeda-Flores Manuel. Distribution functions of multivariate copulas[J]. Statistics and Probability Letters. 2003, 64(1):41-50.
Tibiletti L. Beneficial Changes in Random Variables via Copulas: An Application to Insurance[J]. Insurance: Mathematics and Economics. 1997,19(2):166.
Shemyakin A, Youn H. Bayesian estimation of joint survival functions in life insurance. Working Paper of University of St. Thomas, Saint Paul, MN, USA. 2002.
Frahm G, Junker M, Szimayer A. Elliptical copulas: applicability and limitations[J]. Statistics and Probability Letters. 2003,63(3):275-286.
Cossette H, Gaillardetz P, Marceau é, et al. On two dependent individual risk models[J]. Insurance: Mathematics and Economics. 2002, 30(2):153-166.
Meade Nigel, Islam Towhidul. Modelling the dependence between the times to international adoption of two related technologies[J]. Technological Forecasting
and Social Change. 2003,70(8): 759-778.
Vaz de Melo Mendes Beatriz, Martins de Souza Rafael. Measuring financial risks with copulas[J]. International Review of Financial Analysis. 2004 13: 27-45 .
Bollerslev T, Engle R F, Wooldridge J M. A Capital Asset Pricing Model with Time Varying Covariances[J]. Journal of Political Economy. 1988,96: 116-131.
Kroner K F, Claessens S. Optimal Dynamic Hedging Portfolios and the Currency Composition of External Debt[J]. Journal of International Money and Finance, 1991,10:131-148.
Engle R F, Joseph M. GARCH for Groups[J]. Risk. 1996, 9(8): pp 36-40.
Ding Zh X, Engle R F.Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing. Academia Economic Papers, 2001,29(2):157-184.
Longin F, Solnik B. Is the correlation in international equity return constant: 1960-1990?[J]. Journal of International Money and Finance.1995,14(1):3-26.
Longin F, Solnik B. Extreme Correlation of International Equity Markets[J]. Journal of Finance, 2001,56(2):649-676.
孙炳堃,史道济.二元Cauchy分布尾部的相关性[J].天津大学学报,2000,33(4):432-434.
Hu L. Essays in econometrics with applications in macroeconomic and financial modelling[D]. New Haven: Yale University, 2002.
Joe H. Multivariate Models and Dependence Concepts[M]. London: Chapman & Hall, 1997.
Frees E W, Valdez E A. Understanding Relationships using Copulas[J]. North American actuarial journal, 1998,2 (1): 1-25.
Schmitz, V. Revealing the dependence structure between X(1) and X(n)[J]. Journal of Statistical Planning and Inference. 2004,123(1): 41-47.
Rockinger M, Jondeau E. Conditional dependency of financial series: an application of copulas. Working Paper of Department of Finance, HEC School of Management, Paris, 2001.
Patton A J. Modeling time-varying exchange rate dependence using the conditional copula. Working Paper of Department of Economics, University of California, San Diego, 2001.
Patton A J. Estimation of copula models for time series of possibly different lengths. Working Paper of Department of Economics, University of California,
San Diego, 2001.
Rodriguez J C. Measuring financial contagion: a copula approach. Working Paper of European Institute for Statistics, Probability, Operation Research and their Applications.2003.
朱国庆.金融机构风险测量方法研究[博士学位论文].天津:天津大学,2000.
张尧庭.连接函数（Copula）技术与金融风险分析[J].统计研究,2002, (4):48-51.
史道济,关静. 沪深股市风险的相关性分析[J].统计研究,2003,(10):45-48.
杜本峰,郭兴义.一种新的风险度量工具:PaV及其计算框架[J].统计研究,2003, (2):48-50.
韦艳华,张世英,孟利锋.Copula技术及其在金融时间序列分析上的应用[J].系统工程,2003,21(增刊):41-45.
韦艳华,张世英,孟利锋.Copula理论在金融上的应用[J].西北农林科技大学学报(社会科学版),2003,3(5):97-101.
韦艳华,张世英.金融市场的相关性分析—Copula-GARCH模型及其应用[J].系统工程,2004,22(4):7-12.
韦艳华,张世英,郭焱.金融市场相关程度与相关模式的研究[J].系统工程学报,2004,19(4):355-362.
Patton A J. On the out-of-sample importance of skewness and asymmetric dependence for asset allocation. Working Paper of Department of Economics, University of California, San Diego, 2001.
Bouyé E, Durrleman V, Nikeghbali A, et al. Copulas for finance: a reading guide and some applications. Working Paper of Financial Econometrics Research Centre, City University Business School, London, 2000.
Fisher R A. Statistical Methods for Research Workers[M].1932.
Casella G, Berger R L. Statistical Inference[M]. Duxbury Press, U.S.A.,1990.
Genest C, Mackay J. The joy of Copulas: Bivariate distributions with uniform marginals[J]. American Statistician. 1986,40:280-283.
Genest C. Frank's family of bivariate distributions[J]. Biometrika. 1987,74:549-555.
Genest C, Rivest L P. Statistical inference procedures for bivariate Archimedean copulas[J]. Journal of the American Statistical Association. 1993,88:1034-1043.
Genest C, Ghoudi K, Rivest L P. Discussion of "Understanding relationships
using copulas, by Edward Frees and Emiliano Valdez"[J]. North American Actuarial Journal. 1998,3:143-149.
Schwettzer B, Wolff E. On nonparametric measures of dependence for random variables[J]. Annals of Statistics. 1981,9:879-885.
Coles S, Currie J, Tawn J. Dependence measures for extreme value analyses. Working Paper of Department of Mathematics and Statistics, Lancaster University. 1999.
Juri A. Tail dependence from a distributional point of view. Working paper of Eidgen?ssische Technische Hochschule Zürich Swlss Federal Institute of Technology Zurich, 2002.
Juri A, Wütrich M V. Copula Convergence Theorems for Tail Events[J]. Insurance: Mathematics and Economics, 2002,30:405-420.
Rosenberg J V. Nonparametric pricing of multivariate contingent claim. Working paper of Stern School of Business, New York University. 2000.
Hull J, White A. Value at Risk when daily changes in market variables are nor normally distributed[J]. Journal of Derivatives. 1998,5(3):9-19.
Bouyé E, Ganssel N, Salmon. Investigating Dynamic Dependence Using Copulae. Working Paper of Financial Econometrics Research Centre, City University Business School, London, 2002.
Li W K, Mak T K. On the squared residual autocorrelations in non-linear time series with conditional heteroscedasticity[J]. Journal of Time Series Analysis. 1994,15: 627-636.
Engle R F, Ito T, Lin W L. Meteor showers or heat waves?[J]. Heteroskedastic intra-daily volatility in the foreign exchange market. Econometrica. 1993,58: 525-542.
Karolyi G A. A multivariate GARCH model of international transmissions if stock returns and volatility: the case of the United States and Canada[J]. Journal of Business and Economic Statistics. 1995,13: 11-25.
Jeong J G. Cross-border transmission of stock price volatility: evidence from the overlapping trading hours[J]. Global Finance Journal. 1999,10:53-70.
Brooks C, Henry O T. Linear and non-linear transmission of equity return volatility : evidence from the US，Japan and Australia. Economic Modeling[J]. 2000,17:497-513.
Longin F, Solnik B. Extreme correlation of international equity markets[J].
Journal of Finance, 2001.649-676.
Ramchmand L, Susmel R. Volatility and cross correlation across major stock markets[J]. Journal of Empirical Finance. 1998,5: 397-416.
Ito T, Lin W L. Price volatility and volume spillovers between the Tokyo and New York stock markets. Working Paper of NBER .1994.
Lin W L, Engle R F, Ito T. Do bulls and bears move across borders? International transmission of stock returns and volatility[J]. The Review of Financial Studies. 1994,63: 383-538.
Campbell J Y, Ammer J. What moves the stock and bond markets? A variance decomposition for long-term asset returns[J]. Journal of Finance, 1993,48: 3-37.
Shiller R J, Beltratti A E. Stock prices and bond yields –Can their comovements be explained in terms of present value model?[J]. Journal of Monetary Economics. 1992,30: 25-46.
Cebrian A C, Denuit M, Scaillet O. Testing for Concordance Ordering. Working Paper of University of Zaragoza - General, Catholic University of Louvain (UCL) - General and HEC Geneve UNI MAIL .2002
Denuit M, Scaillet O. Nonparametric Tests for Positive Quadrant Dependence. Working Paper of Catholic University of Louvain (UCL) - General and HEC Geneve UNI MAIL. 2002.
Das S R, Geng G. Correlated Default Processes: A Criterion-Based Copula Approach. Working Paper of Leavey School of Business, Santa Clara University .2004.
Yu F. Dependent Default in Intensity-Based Models. Working Paper of University of California, Irvine - Finance Area. 2003.
Junker M, Szimayer A, Wagner N. Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications. Working Paper of Financial Engineering Group, Center of Advanced European Studies and Research, Germany (CAESAR). 2003.
Chen X H, Fan Y Q, Patton A J. Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates. Working Paper of Department of Economics, New York University. 2004.
Rosenberg J V, Schuermann T. A General Approach to Integrated Risk Management with Skewed, Fat-Tailed Risk. Working Paper of Research and
Market Analysis Group, Federal Reserve Bank of New York .2004.
Granger C W J, Terasvirta T, Patton A J. Common Factors in Conditional Distributions for Bivariate Time Series. Working Paper of University of California, San Diego - Department of Economics, 2004.
Quintos C . Estimating Tail Dependence and Testing for Contagion Using Tail Indices. Working Paper of University of Rochester - William E. Simon Graduate School of Business Administration. 2001.
Wise M B, Bhansali V. Implications of Correlated Default for Portfolio Allocation to Corporate Bonds. Working Paper of California Institute of Technology - General and Pacific Investment Management Company (PIMCO) - General, 2002.
Malevergne Y, Sornette D. Testing the Gaussian Copula Hypothesis for Financial Assets Dependences. Working Paper of University of Nice and UCLA and LPMC. 2001.
Schonbucher P, Schubert D. Copula-Dependent Defaults in Intensity Models. Working Paper of Department of Mathematics and KPMG, Swiss Federal Institute of Technology Zurich. 2002.
Jondeau E, Rockinger M. Conditional Dependency of Financial Series: The Copula-GARCH Model. Working Paper of Economic Study and Research Division, Banque de France. 2003.
Dhaene J, Denuit M, Goovaerts M, et al. The Concept of Comonotonicity in Actuarial Science and Finance: Theory. Working Paper of Department of Applied Economics, Katholieke Universiteit Leuven (KUL). 2003.
Mandelbrot B. The Variation of certain speculative prices[J]. Journal of Business. 1963,36:394-419.
Fama E F. The behavior of stock market prices[J]. Journal of Business. 1965, 38: 34-105
李汉东.多变量时间序列持续性研究[博士学位论文].天津:天津大学,2000.
柯珂.ARCH模型族的建模研究[硕士学位论文].天津:天津大学, 2000.
柯珂,张世英.ARCH模型的诊断分析[J].管理科学学报,2001,4(2):12-18.
杜子平.基于波动模型的金融市场分析[博士学位论文].天津:天津大学,2002.
Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility models［J］. Journal of Business & Economic Statistics. 1994, 12: 371-388.
Hull J, White A. The pricing of options on assets with stochastic volatilities[J].
The Journal of Finance. 1987, XLII(2): 281-299.
Melino A, Turnbull S M. Pricing foreign currency options with stochastic volatility[J]. Journal of Econometrics. 1990, 45: 239-265.
Harvey A C. Long memory in stochastic volatility. Working Paper of London School of Economics.1993.
Kim S, Shephard N, Chib S. Stochastic volatility: likelihood inference and comparison with ARCH models[J]. Review of Economic Studies. 1998,65: 361-393.
Board J L G, Sandmann G, Sutcliffe C M S. The effect of contemporaneous futures market volume on spot market volatility. Working Paper of London School of Econometrics. 1997.
Ghysels E, Goureroux C, Jasiak J. Stochastic volatility and time deformation: an application to trading volume and leverage effects. Working Paper of Univerite de Montreal. 1996.
Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility models with fat-tail and correlated errors[J]. Journal of Business & Economic Statistics. 1994, 12: 371-388.
Ruiz E. Quasi-maximum likelihood estimation of stochastic volatility models[J]. Journal of Econometrics. 1994, 63: 289-306.
Watanabe T. A non-linear filtering approach to stochastic volatility models with an application to daily stock returns[J]. Journal of Applied Econometrics. 1999, 14: 101-121.
Danielsson J. Stochastic volatility in asset prices: estimation with simulated maximum likelihood[J]. Journal of Econometrics. 1994, 61: 375-400.
Danielsson J, Richard J F. Accelerated Gaussian importance sampler with application to dynamic latent variable models, Journal of Applied Econometrics[J]. 1993, 8: 153-173.
Andersen T. Chung H, Sorensen B. Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study[J]. Journal of Econometrics. 1999,91:61-87.
Meyer R, Yu J. Bugs for a Bayesian analysis of stochastic volatility models[J]. Econometrics Journal. 2000,3:198-215.
Yu J. MCMC methods for estimating stochastic volatility models with leverage effect: comments on Jacquier, Polson and Rossi. Working Paper of Department
of Economics, University of Auckland, New Zealand.2002.
Hennessy D, Lapan H E. The Use of Archimedean Copulas to Model Portfolio Allocations[J]. Mathematical Finance. 2002, 12: 143-154.
Smith M. Modeling Sample Selection Using Archimedean Copulas[J]. Econometrics Journa.2003, 6: 99-123.
Taylor S J, Wang Y H. Option Prices and Risk-Neutral Densities for Currency Cross-Rates. Working Paper of Department of Accounting and Finance, Lancaster University .2004.
Valdez E A. Bivariate ananlysis of survivorship and persistency[J]. Insurance: Mathematics and Economics. 2001,29:357-373.
Xu Y. Modelling dependence between financial returns with copulas and stochastic volatility marginal. Working Paper of Department of Economics, University of Miami. 2003.
Anderson T W. Maximum likelihood estimates for a multivariate Normal distribution when some observations are missing[J]. Journal of the American Statistical Association. 1957,52:200-203.
Little R J A, George C. Theory of point estimation[M]. New York: Springer, 1998.
Stambaugh R F. Analyzing investments whose histories differ in length[J]. Journal of Financial Economics, 1997,45:285-331.
Diebold F X, Gunther T, Tay A S. Evaluating density forecasts with applications to financial risk management[J]. International Economic Review, 1998,39:863-883.
Diebold F X, Hahn J, Tay A S. Multivariate density forecast evaluation and calibration in financial risk management: high-frequency returns on foreign exchange[J]. The Review of Economics and Statistics, 1999,81(4):661-673.
Shao J. Mathematical statistics[M].New York: Springer, 1999.
吴喜之,王兆军.非参数统计方法[M].北京:高等教育出版社,1996.
Klugman S A, Parsa R. Fitting bivariate loss distributions with copulas[J]. Insurance: Mathematics and Economics. 1999,24(1-2): 139-148.
Christoffersen P F. Evaluating interval forecasts[J]. International Economic Review, 1998,39(4):841-862.
Engel R B, Manganelli S. CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles. Working Paper of Department of Economics,
University of California, San Diego.1999.
Goorbergh R W J, Genest C, Werker B J M. Multivariate option pricing using dynamic copula models. Working Paper of Department of Finance and Center for Economic Research, Tilburg University. 2003.
Bollerslev T, Mikkelsen H O. Modeling and pricing long memory in stock market volatility[J]. Journal of Econometrics, 1996,73:151-184.
Ding Z, Granger C W J, Engle R F. A long memory property of stock market returns and a new model[J]. Journal of Empirical Finance, 1993,1:83-106.
苏卫东,张世英.随机波动模型分析及其在上海股市的应用[J]. 系统工程理论方法应用,2001,10(3):202-206.
Lamoureux C G, Lastrapes W D. Persistence in variance, structural change, and the GARCH model[J]. Journal of Business & Economic Statistic, 1990,8:225-234.
苏卫东.金融波动模型及其在中国股市的应用[博士学位论文].天津:天津大学,2002
苏卫东,张世英. 变截距SV模型及其在上海股市的实证. 系统工程理论方法应用, 2002,12(3):57-63
孙青华. 长记忆向量时间序列协整建模理论与变结构研究[博士学位论文]. 天津: 天津大学,1999.
孙金丽. 变结构波动建模及其应用[硕士学位论文]. 天津: 天津大学,2003.
白崑. 随机波动模型及其应用[硕士学位论文]. 天津: 天津大学,2002.
郭名媛. 具有马尔可夫结构转换机制的波动模型及其应用[硕士学位论文]. 天津: 天津大学,2003.
徐梅. 金融波动分析的小波和频域方法研究[博士学位论文]. 天津: 天津大学,2003.
Dueker. Markov switching in GARCH processes and mean reverting stock market volatility[J]. Journal of Business and Economic Statistics , 1997(1):45-69.
Cai. A Markov model of switching-regime ARCH[J]. Journal of Business and Economic Statistics, 1994(12):309-316.
Kalimipalli, Susmel. Regime-switching stochastic volatility and short-term interest rates. Working Papers.2002.
Forbes K, Rigobon R. No contagion, only interdependence: measuring stock markets comovements[J]. Journal of Finance, 2002,57(5):2223-2261.
Baig T, Goldfaijn I. Financial market contagion in the Asian crisis. Working Paper of IMF Staff. 1998.
Ellis L, Lewis E. The response of financial markets in Australia and New Zealand to News about the Asian crisis. BIS Conference on International Financial Markets and Implications for Monetary and Financial Stability, Basle. 1999,8:25-26.
Dungey M, Zhumabekova D, Scholar V. Testing for contagion using correlations: some words of caution. Working Paper of Pacific Basin, 2001.
Pedhazur E J. Multiple regression in behavioral research[M]. Orlando: Harcourt Brace College Publishers, 1997.
黄违洪,张世英.模型结构变化点检测法[J]. 应用数学学报, 1987, 10(3):267-275.
Kim D. A Bayesian significance test on the stationarity of regression parameters[J]. Biometrika, 1991,78:667-675.
Kim D, Kon S J. Structural change and time dependence in models of stock returns[J]. Journal of Empirical Finance, 1999, (9):283-308.
Lindley D V. Introduction to Probability and Statistics from a Bayesian Viewpoint. Vol. 2.Cambridge University Press, Cambridge.1965.
Box G E P, Tiao G C. Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, MA. 1973.
Cherubini U, Luciano E. Value-At-Risk Trade-Off and Capital Allocation with Copulas. Working Paper of Department of Statistics and Applied Mathematics, Polyhedron Computational Finance and University of Turin. 2001.
Schonbucher P. Taken to the Limit: Simple and Not-So-Simple Loan Loss Distributions Working Paper of Department of Mathematics, Swiss Federal Institute of Technology Zurich. 2003.
Tibiletti L. The Riskier the Assets, the Riskier the Portfolios: Pitfalls and Misinterpretations. Working Paper of Department of Statistics and Applied Mathematics, University of Turin. 2003.
Glasserman P, Heidelberger P, Shahabuddin P. Portfolio Value-at-Risk with Heavy-Tailed Risk Factors. Working Paper of Graduate School of Business, Columbia University, New York.2000.
Frey R. Dependent Defaults in Models of Portfolio Credit Risk. Working Paper of Department of Mathematics, University of Leipzig. 2003.
Embrechts P A, McNeil A, Straumann D. Correlation and Dependence in Risk Management: Properties and Pitfalls. Working Paper.1999.
Clemente A D, Romano C. Measuring portfolio Value-at-Risk by a copula-EVT based approach. Working Paper of University of Rome "La Sapienza", 2003.
Rosenberg J, Schuermann T. A General Approach to Integrated Risk Management with Skewed, Fat-tailed Risks. Working Paper of Federal Reserve Bank of New York, 2004.
Rank J, Siegl T. Applications of copulas for the calculation of Vaule-at-Risk. Working Paper. 2003.
Romano C. Applying copula function to risk mangement. Working Paper of University of Rome "La Sapienza", 2002
Devroye. Non-uniform random variate generation[M]. New York: Springer-Verlag, 1986.
Bertero E, Colin M. Structure and Performance: Global Interdependence of Stock Markets Around the Crash of October 1987. Working Paper of C.E.P.R. 1989.
King M, Wadhwani S. Transmission of Volatility Between Stock Markets. Review of Financial Studies.1990.
Calvo S, Reinhart C. Capital Flows to Latin America: Is There Evidence of Contagion Effects? Working Paper.1996.
Longin F, Solnik B. Is the Correlation in International Equity Returns Constant: 1960-1990?[J]. Journal of International Money and Finance. 1995,14: 3-26.
Hartman P, Straetmans S, de Vries C. Asset market linkages in crisis periods. Working Paper of Erasmus, 2000.
Ang A, Bekaert G. International Asset Allocation with Regime Shifts[J]. Review of Financial Studies. 2002,15(4):1137-1187.
Chesney F, Jondeau E. Does Correlation Between Stock Returns Really Increase During Turbulent Period? Working Paper of Banque de France, 2000.