基于有限混合状态空间的金融随机波动模型及应用研究
|
摘要
近年来,金融随机波动(SV)模型广泛地应用于金融经济学、数理金融学和计量经济学领域,专门用以捕捉金融市场金融资产时变波动性,并对金融决策制定产生重要的影响,是现代金融学理论界与实务界中一种非常重要的波动模型。目前SV模型在金融计量学界正方兴未艾,虽然取得了一系列的研究成果,但计算上较为简单、而算法相对有效的估计方法迄今研究不足。
本文对已有研究文献进行了广泛的调研和系统的综述,重点讨论SV模型、扩展模型和马尔科夫转移SV模型的近似估计,并对我国沪深股票收益率和市场短期利率展开实证分析,论文主要工作和创新如下:
一、讨论了高斯混合状态空间模型、马尔科夫转移状态空间模型以及马尔科夫转移高斯混合状态空间模型的确切分析,推导了这些模型的确切滤波、确切似然函数,依次提出了依赖于控制参数的三种近似滤波,以及相应的近似似然函数和近似平滑技术,并通过随机模拟实验讨论了近似估计方法的准确性。
二、基于高斯混合近似滤波方法给出了SV模型、扩展SV模型和马尔科夫转移SV模型的近似估计方法;通过随机模拟实验,将近似估计方法与粒子滤波方法、传统估计方法进行了拟合准度分析,参数估计有限样本性质分析,从而评估了近似估计方法应用于SV模型的可行性。
三、利用SV类模型分析了沪深股市收益率、短期拆借利率序列的时变波动性,证明了SV模型比GARCH类模型具有更好的预测能力,证明了近似方法与贝叶斯方法和蒙特卡罗似然具有可比性,证实了沪深股市波动性、短期利率波动性中均存在明显的区制转移特征,证实了忽略波动结构性突变可能导致波动持续性高估的事实,并且发现利率波动不仅存在均值转移,还存在波动持续性和波动的波动转移,而且这种波动转移性与我国经济增长率变化有一定的联系。
In recent years, stochastic volatility (SV) class of models are widely used in areas offinancial economics and mathematical finance. They can capture time-varying volatilities offinancial assets, and have important impacts on financial decision-making. The developmentof SV models is highly interdisciplinary, covering relevant theories and contents of financialeconomics, probability and statistics theory, and econometrics. They provide us with help tounderstand methods and models of real option pricing, e?ective asset allocation and accuraterisk assessment. As e?ective methods for describing time-varying volatility of an financialassets, the studies on the SV models have important theoretical significance and practicalsignificance.
The SV class of models is a basic alternative to autoregressive conditional heteroscedastic(GARCH) class of models, but they provide a more ?exible structure for describing the time-varying volatility. As the model adds an error term in the dynamics of volatility introducinganother source of randomness, it has been found to fit asset returns better, have residualscloser to standard normal and have better statistical properties. However, they are typicalnonlinear non-Gaussian state space models, with the exact likelihood function being a highlycomplex and high-dimensional integration in analytical, leading to parameters and latent log-volatilities very di?cult to estimate. Although several extended SV models can be furtherused to examine some practical problems, such as asymmetric e?ect or leverage e?ect betweenvolatilities and returns, volatility clustering, volatility persistence and structural break, theyare more complex and thus too di?cult to estimate. Thus, searching for a computationallysimple and algorithmically e?ective estimation method is still the subject to explore in financialeconometrics, but also a major concern in this article.
This paper carries out a series of studies around SV models. Facing some problems fromthe basic SV model and their extension, we review and sum up past researches, carding thetheoretical relation between SV models and modern finance. We mainly discuss estimationmethods for the basic SV model, extended SV models and the Markov-switching SV model.Then these models are applied to return data of China’s Shanghai and Shenzhen stock market,and short-term lending interest rate of bank credit market.
In many parameter estimation methods for the basic SV model, some studies advocateto use the Markov chain Monte Carlo procedure or the simulated expected maximum pro- cedure, through taking the square and the logarithm of the SV model, and approximatingthe log-chi-square distribution by a mixture of normal distributions. However, the maximumlikelihood estimation procedure for this transformed SV model has not yet been put forward.Not only that, but approximate estimation of the coupled model for Gaussian mixture process,Markov switching process and state space process has also not been presented in time serieseconometrics. Based on the exact analysis of Gaussian mixture state space model, Markovswitching state space model, and Markov switching Gaussian mixture state space model, wedevelop three approximate filters, i.e. AMF(k), MSAMF(k), and MSMIXAMF(k) respectively,and the corresponding approximate maximum likelihood estimators and smoothing techniques.With these approximate filter, approximate maximum likelihood estimator and approximatesmoothing, this paper presents estimation methods for the basic SV model, the extended SVmodel, and the Markov switching SV model. The approximate estimation results are alsocompared to the results from the particle filter.
The proposed approximate methods are examined by many simulation analysis usingsimulated data and repeated trials. The results show that our methods for Gaussian mixturestate space model, Markov switching state space model, and their coupled model work quitewell. The approximate filters have high accuracy, with the fitted results to the true stateprocess closing to the exact filters. Even with a smaller value of parameter k, they are also veryaccurate. Moreover, simulation results from the Gaussian mixture state space model also showthat parameter estimates are almost same under di?erent k using the approximate maximumlikelihood estimator. Similarly, simulation experiments for the basic SV model show that theapproximate filter (AMF) is very close to the particle filter, better than the Monte Carlolikelihood (MCL) filter (Koopman & Uspensky, 2002) when the number of simulation is smalland the Kalman filter. For the sample performance of parameter estimates, our approximatemaximum likelihood (AML) estimator performs competitively with the MCL estimtor when thenumber of simulation is large and the N-ML estimtor suggested by Fridman & Harris (1998),better than the QMl estimator based on the Kalman filter. At last, simulation experimentsfor the Markov switching SV model show that the approximate filter MSMIXAMF(k) notonly can better fit to the log-volatility process than MSAMF(k), but also can well describethe hidden Markov process under the true data generation process. Moreover, it is shownthat the approximate filter for the Markov switching Gaussian mixture state space model,MSMIXAMF(k), is obviously much better than that for the Markov-switching state spacemodel, MSAMF(k), while the latter will be the Kim approximate filter suggested by Kim(1994) when k = 1.
Equipped with the SV models and the approximate methods introduced in this study, wecarried out empirical analysis on returns of China’s Shanghai and Shenzhen stock market andshort-term bank lending rate. On the one hand, we compare the in-sample performance of time-varying volatilities with di?erent models and di?erent estimation methods. Firstly, the fittedresults from GARCH-type models and SV-type models with return data and short-term interestrate data show that the SV models have higher explanatory power in modeling time-varying volatility, with stronger tail fitting e?ect. Secondly, we implement Bayesian Markov chainMonte Carlo estimation (JPR estimator and KSC estimator), QML estimator, MCL estimatorand proposed AML estimator for the basic SV model. It is shown that our AML estimatorperforms competitively with the Bayesian estimation methods and the MCL estimator. Theresults from the particle filter further show that the AML estimator is slightly better thanthe Bayesian estimation methods and the MCL estimator. Finally, with introducing leveragee?ects and regime switching, we compare in-sample performance of the basic SV model, theasymmetric SV model and the Markov switching SV model to stock returns and short terminterest rate.
On the other hand, this study e?ectively tests and describes dynamic characteristics ofChina’s stock returns and short-term interest rate using di?erent SV models, so as to provideus with basic results for financial risk management and decision-making. First of all, althoughthe Shanghai stock returns and Shenzhen stock returns share a common trend at the majorityof periods, the di?erences between them can be described by the GARCH-type models and theSV-type models. For instance, Shanghai stock market has obvious leverage e?ect, while thereis no leverage e?ects in Shenzhen stock market. Both stock market volatilities of Shanghaiand Shenzhen have obvious regime-switching characteristics. In the majority of time periodsregime shifts are the same for them, but in 1995 and early 1996 Shanghai stock market takesa high-volatility regime, while Shenzhen stock market is in a low-volatility regime. Secondly,level e?ects are found between the time-varying volatility and the level of short-term interestrate, the estimated values of them are less than one using the SV-type models. Moreover,the results from the asymmetric SV model show the existence of leverage e?ect between theinterest rate volatility and interest rates, and the results from the Markov switching SV modelsshow obvious regime shifts in interest rate volatility. Finally, the results also show that interestrate volatilities not only have regime switching between high and low volatilities, but also haveobvious regime shifts between volatility consistence and volatility of volatility at the sametime. Thus our study reveals an internal mechanism that the short-term lending rate volatilitychange between a low volatility - low persistence - high volatility of volatility regime and a highvolatility - high persistence - low volatility of volatility regime. In addition, this study also findthat the regime switching characteristics have an obvious linkage with the GDP growth rate inChina’s macroeconomy, which further demonstrates the importance of interest rate volatility.
本文对已有研究文献进行了广泛的调研和系统的综述,重点讨论SV模型、扩展模型和马尔科夫转移SV模型的近似估计,并对我国沪深股票收益率和市场短期利率展开实证分析,论文主要工作和创新如下:
一、讨论了高斯混合状态空间模型、马尔科夫转移状态空间模型以及马尔科夫转移高斯混合状态空间模型的确切分析,推导了这些模型的确切滤波、确切似然函数,依次提出了依赖于控制参数的三种近似滤波,以及相应的近似似然函数和近似平滑技术,并通过随机模拟实验讨论了近似估计方法的准确性。
二、基于高斯混合近似滤波方法给出了SV模型、扩展SV模型和马尔科夫转移SV模型的近似估计方法;通过随机模拟实验,将近似估计方法与粒子滤波方法、传统估计方法进行了拟合准度分析,参数估计有限样本性质分析,从而评估了近似估计方法应用于SV模型的可行性。
三、利用SV类模型分析了沪深股市收益率、短期拆借利率序列的时变波动性,证明了SV模型比GARCH类模型具有更好的预测能力,证明了近似方法与贝叶斯方法和蒙特卡罗似然具有可比性,证实了沪深股市波动性、短期利率波动性中均存在明显的区制转移特征,证实了忽略波动结构性突变可能导致波动持续性高估的事实,并且发现利率波动不仅存在均值转移,还存在波动持续性和波动的波动转移,而且这种波动转移性与我国经济增长率变化有一定的联系。
In recent years, stochastic volatility (SV) class of models are widely used in areas offinancial economics and mathematical finance. They can capture time-varying volatilities offinancial assets, and have important impacts on financial decision-making. The developmentof SV models is highly interdisciplinary, covering relevant theories and contents of financialeconomics, probability and statistics theory, and econometrics. They provide us with help tounderstand methods and models of real option pricing, e?ective asset allocation and accuraterisk assessment. As e?ective methods for describing time-varying volatility of an financialassets, the studies on the SV models have important theoretical significance and practicalsignificance.
The SV class of models is a basic alternative to autoregressive conditional heteroscedastic(GARCH) class of models, but they provide a more ?exible structure for describing the time-varying volatility. As the model adds an error term in the dynamics of volatility introducinganother source of randomness, it has been found to fit asset returns better, have residualscloser to standard normal and have better statistical properties. However, they are typicalnonlinear non-Gaussian state space models, with the exact likelihood function being a highlycomplex and high-dimensional integration in analytical, leading to parameters and latent log-volatilities very di?cult to estimate. Although several extended SV models can be furtherused to examine some practical problems, such as asymmetric e?ect or leverage e?ect betweenvolatilities and returns, volatility clustering, volatility persistence and structural break, theyare more complex and thus too di?cult to estimate. Thus, searching for a computationallysimple and algorithmically e?ective estimation method is still the subject to explore in financialeconometrics, but also a major concern in this article.
This paper carries out a series of studies around SV models. Facing some problems fromthe basic SV model and their extension, we review and sum up past researches, carding thetheoretical relation between SV models and modern finance. We mainly discuss estimationmethods for the basic SV model, extended SV models and the Markov-switching SV model.Then these models are applied to return data of China’s Shanghai and Shenzhen stock market,and short-term lending interest rate of bank credit market.
In many parameter estimation methods for the basic SV model, some studies advocateto use the Markov chain Monte Carlo procedure or the simulated expected maximum pro- cedure, through taking the square and the logarithm of the SV model, and approximatingthe log-chi-square distribution by a mixture of normal distributions. However, the maximumlikelihood estimation procedure for this transformed SV model has not yet been put forward.Not only that, but approximate estimation of the coupled model for Gaussian mixture process,Markov switching process and state space process has also not been presented in time serieseconometrics. Based on the exact analysis of Gaussian mixture state space model, Markovswitching state space model, and Markov switching Gaussian mixture state space model, wedevelop three approximate filters, i.e. AMF(k), MSAMF(k), and MSMIXAMF(k) respectively,and the corresponding approximate maximum likelihood estimators and smoothing techniques.With these approximate filter, approximate maximum likelihood estimator and approximatesmoothing, this paper presents estimation methods for the basic SV model, the extended SVmodel, and the Markov switching SV model. The approximate estimation results are alsocompared to the results from the particle filter.
The proposed approximate methods are examined by many simulation analysis usingsimulated data and repeated trials. The results show that our methods for Gaussian mixturestate space model, Markov switching state space model, and their coupled model work quitewell. The approximate filters have high accuracy, with the fitted results to the true stateprocess closing to the exact filters. Even with a smaller value of parameter k, they are also veryaccurate. Moreover, simulation results from the Gaussian mixture state space model also showthat parameter estimates are almost same under di?erent k using the approximate maximumlikelihood estimator. Similarly, simulation experiments for the basic SV model show that theapproximate filter (AMF) is very close to the particle filter, better than the Monte Carlolikelihood (MCL) filter (Koopman & Uspensky, 2002) when the number of simulation is smalland the Kalman filter. For the sample performance of parameter estimates, our approximatemaximum likelihood (AML) estimator performs competitively with the MCL estimtor when thenumber of simulation is large and the N-ML estimtor suggested by Fridman & Harris (1998),better than the QMl estimator based on the Kalman filter. At last, simulation experimentsfor the Markov switching SV model show that the approximate filter MSMIXAMF(k) notonly can better fit to the log-volatility process than MSAMF(k), but also can well describethe hidden Markov process under the true data generation process. Moreover, it is shownthat the approximate filter for the Markov switching Gaussian mixture state space model,MSMIXAMF(k), is obviously much better than that for the Markov-switching state spacemodel, MSAMF(k), while the latter will be the Kim approximate filter suggested by Kim(1994) when k = 1.
Equipped with the SV models and the approximate methods introduced in this study, wecarried out empirical analysis on returns of China’s Shanghai and Shenzhen stock market andshort-term bank lending rate. On the one hand, we compare the in-sample performance of time-varying volatilities with di?erent models and di?erent estimation methods. Firstly, the fittedresults from GARCH-type models and SV-type models with return data and short-term interestrate data show that the SV models have higher explanatory power in modeling time-varying volatility, with stronger tail fitting e?ect. Secondly, we implement Bayesian Markov chainMonte Carlo estimation (JPR estimator and KSC estimator), QML estimator, MCL estimatorand proposed AML estimator for the basic SV model. It is shown that our AML estimatorperforms competitively with the Bayesian estimation methods and the MCL estimator. Theresults from the particle filter further show that the AML estimator is slightly better thanthe Bayesian estimation methods and the MCL estimator. Finally, with introducing leveragee?ects and regime switching, we compare in-sample performance of the basic SV model, theasymmetric SV model and the Markov switching SV model to stock returns and short terminterest rate.
On the other hand, this study e?ectively tests and describes dynamic characteristics ofChina’s stock returns and short-term interest rate using di?erent SV models, so as to provideus with basic results for financial risk management and decision-making. First of all, althoughthe Shanghai stock returns and Shenzhen stock returns share a common trend at the majorityof periods, the di?erences between them can be described by the GARCH-type models and theSV-type models. For instance, Shanghai stock market has obvious leverage e?ect, while thereis no leverage e?ects in Shenzhen stock market. Both stock market volatilities of Shanghaiand Shenzhen have obvious regime-switching characteristics. In the majority of time periodsregime shifts are the same for them, but in 1995 and early 1996 Shanghai stock market takesa high-volatility regime, while Shenzhen stock market is in a low-volatility regime. Secondly,level e?ects are found between the time-varying volatility and the level of short-term interestrate, the estimated values of them are less than one using the SV-type models. Moreover,the results from the asymmetric SV model show the existence of leverage e?ect between theinterest rate volatility and interest rates, and the results from the Markov switching SV modelsshow obvious regime shifts in interest rate volatility. Finally, the results also show that interestrate volatilities not only have regime switching between high and low volatilities, but also haveobvious regime shifts between volatility consistence and volatility of volatility at the sametime. Thus our study reveals an internal mechanism that the short-term lending rate volatilitychange between a low volatility - low persistence - high volatility of volatility regime and a highvolatility - high persistence - low volatility of volatility regime. In addition, this study also findthat the regime switching characteristics have an obvious linkage with the GDP growth rate inChina’s macroeconomy, which further demonstrates the importance of interest rate volatility.
引文
[1]林海、郑振龙:《中国利率期限结构:理论及应用》,中国财经出版社,2004年。
[2]张世英、樊智:《协整理论与波动模型――金融时间序列分析及应用》,清华大学出版社,2004年。
[3] Abramowitz M., Stegun N. Handbook of Mathematical Functions[M]. Dover Publications,NY, 1970.
[4] Anderson B D O., Moore J B. Optimal Filtering[M]. Prentice Hall, Englewood Cli?s NJ,1979.
[5] Bhar R., Hamori S. Hidden Markov Models: Applications to Financial Economics[M].Dordrecht: Kluwer Academic, 2004.
[6] Bingham N H., Kiesel R. Risk-Neutral Valuation: Pricing and Hedging of FinancialDerivatives[M]. Springer Finance, London, 1998.
[7] Bjo¨rk T. Arbitrage Theory in Continuous Time[M]. Oxford University Press, 1998.
[8] Cappa′O., Moulines E., Ryd′en T. Inference in Hidden Markov Models[M]. Springer Seriesin Statistics. New York: Springer, 2005.
[9] Du?e D. Security Markets: Stochastic Models[M]. Academic Press, Boston, 1988.
[10] Durbin J., Koopman S J. Time Series Analysis by State Space Methods[M]. OxfordUniversity Press: Oxford, 2001.
[11] Engle R., Lee G. A long-run and short-run component model of stock return volatility.in Cointegration, Causality and Forecasting[M], edited by Engle R. and White H., OxfordUniversity Press, 1999.
[12] Fru¨hwirth-Schnatter S. Finite Mixture and Markov Switching Models[M]. Springer NewYork, 2006.
[13] Fuller W A. Introduction to Time Series (2nd edn)[M]. John Wiley, New York, 1996.
[14] Granger C W J., Tera¨asvirta T. Modelling Nonlinear Economic Relationships[M]. Oxford:Oxford University Press, 1993.
[15] Harvey A. Forecasting Structural Time Series Models and the Kalman Filter[M]. Cam-bridge University Press, Cambridge et al, 1990.
[16] Jackson J. A User’s Guide to Principal Components[M]. John Wiley, 1991.
[17] Kim C J., Nelson C R. State Space Models with Regime Switching, Classical and GibbsSampling Approaches with Applications[M]. Cambridge, MA: MIT Press, 1999.
[18] Krolzig H M. Markov-Switching Vector Autoregressions: Modelling, Statistical In-ference, and Application to Business Cycle Analysis[M]. New York/Berlin/Heidelberg:Springer,1997.
[19] Lemke W. Term Structure Modelling and Estimation in a State Space Framework[M].Springer, Berlin et al, 2006.
[20] Ripley B D. Stochastic Simulation[M]. John Wiley: New York, 1987.
[21] Taylor S J. Modeling Financial Time Series[M]. John Wiley: New York, 1986.
[22] Titterington D M., Smith A F M., Makov U E. Statistical analysis of finite mixturedistributions[M]. Chichester: John Wiley, 1985.
[23] Tsay R S. Analysis of Financial Time Series (2nd Edition)[M]. John Wiley and Sons,Inc, 2005.
[24] Wong C K J. Latent factor models of high frequency financial time series. UnpublishedPhD Thesis. University of Oxford, 2002.
[1] Anderson H M., Nam K., Vahid F. Asymmetric nonlinear smooth transition GARCHmodels. In Rothman P. (Ed.), Nonlinear Time Series Analysis of Economic and FinancialData, Boston: Kluwer, 1999: 191-207.
[2] Bansal R., Gallant A R., Hussey R., Tauchen G E. Computational aspects of nonparamet-ric simulation estimation. In Belsey D A. (Ed.), Computational Techniques for Econometricsand Economic Analysis. Boston, MA: Kluwer Academic Publishers, 1993: 3-22.
[3] Bates D S. Testing option pricing models. In Maddala G S., Rao C R. (Ed.), Handbookof Statistics, v. 14: Statistical Methods in Finance, Elsevier, Amsterdam, 1996a: 567-611.
[4] Black F. Studies in stock price volatility changes. Proceedings of the 1976 Business Meet-ing of the Business and Economic Statistics Section, American Statistical Association, 1976:177-181.
[5] Diebold F X., Lee J H., Weinbach G C. Regime switching with time-varying transitionprobabilities. In Hargreaves C P. (Ed.), Nonstationary Time Series Analysis and Cointegra-tion, 1994: 283-302. Oxford: Oxford University Press.
[6] Engle R F., Lee G. Estimating di?usions models of stochastic volatility. In Rossi P E.(Ed.), Modelling Stock Market Volatility: Bridging the Gap to Continuous Time, 1996: 333-355. San Diego: Academic Press.
[7] Gamerman D., Smith A F M. Bayesian analysis of longitudinal data studies. In BernardoJ M., Berger J O., Dawid A P., Smith A F M. (Ed.), Bayesian Statistics, 5, 1996: 587-597.Oxford: Oxford University Press.
[8] Hamilton J. State-space models. In Engle R., McFadden D. (Ed.), Handbook of Econo-metrics Volume 4, 1994: 3039-3080. Amsterdam: North-Holland.
[9] Harvey A C. Long-memory in stochastic volatility. In Knight J., Satchell S. (Ed.), Fore-casting Volatility in Financial Markets. Oxford: Butterworth-Heineman, 1998: 307-320.
[10] Jacquier E., Polson N G., Rossi P E. Stochastic volatility: univariate and multivariate ex-tensions. Computing in Economics and Finance 112, Society for Computational Economics,1999.
[11] Palm F. Garch models of volatility. In ByMaddala G., Rao C. (Ed.), Handbook of Statis-tics, 1996: 209-240, Elsevier Science, Amsterdam.
[12] Pen?a D., Guttman I. Bayesian approach to robustifying the Kalman filter. In Spall J C.(Ed.), Bayesian Analysis of Time Series and Dynamic Linear Models, 1988: 227-253. NewYork: Marcel Dekker.
[13] Schnatter S., Gutknecht D., Kirnbauer R. A Bayesian approach to estimating the pa-rameters of a hydrological forecasting system. In Viertl R. (Ed.), Probability and BayesianStatistics, 1987: 415-422. New York: Plenum.
[14] Shephard N G. Statistical aspects of ARCH and stochastic volatility. in Cox D R.,Bamdor?-Nielson 0 E., Hinkley D V. (Ed.), Time Series Models in Econometrics, Financeand Other Fields (London: Chapman & Hall),1996: 1-67.
[15] Taylor S J. Financial returns modeled by the product of two stochastic processes, a studyof daily sugar prices 1961-79. In Time Series Analysis: Theory and Practice 1, AndersonOD (Ed.). North-Holland: Amsterdam, 1982: 203-226.
[1]白崑、张世英:扩展SV模型及其在深圳股票市场的应用[J],《系统工程》2001年第19卷第6期。
[2]曹阳、李剑武:人民币实际汇率水准波动对进出口贸易的影响-基于1980-2004年的实证研究[J],《世界经济研究》2006年第150期。
[3]陈敏、王国明、吴国富、蒋学雷:中国证券市场的ACD-GARCH模型及其应用[J],《统计研究》2003年第11期。
[4]董乐:我国短期利率均值回复假设的实证研究[J],《数量经济技术经济研究》2006年第11期。
[5]杜子平、张世英:SV模型的聚合及其边际化研究[J],《系统工程理论方法应用》2002年第11卷第2期。
[6]范龙振:上交所债券利率期限结构与两因子Vasicek模型[J],《复旦学报(自然科学版)》2003年第5期。
[7]韩伟、李钢:高频金融数据的长记忆SV模型分析――基于FFF回归[J],《西北农林科技大学学报(社会科学版)》2006年第6卷第2期。
[8]洪永淼、林海:中国市场利率动态研究――基于短期国债回购利率的实证分析[J],《经济学(季刊)》2006年第5期。
[9]蒋祥林、王春峰、吴晓霖:基于状态转移ARCH模型的中国股市波动性研究[J],《系统工程》2004年第3期。
[10]柯珂、张世英:ARCH模型的诊断分析[J],《管理科学学报》2001年第4期。
[11]李成、马国校:VaR模型在我国银行同业拆借市场中的应用研究[J],《金融研究》2007年第5期。
[12]李付军:SV-GED模型在中国股市的VaR与ES度量及分析[J],《系统工程理论方法应用》2006年第15卷第1期。
[13]李汉东、张世英:随机波动模型的持续性和协同持续性研究[J],《系统工程学报》2002年第17卷第4期。
[14]李汉东、张世英:ARCH模型与SV模型之间的关系研究[J],《系统工程学报》2003年第18卷第2期。
[15]刘丹红、张世英、黄涛、蒋孝胜:LMSV模型波动的长记忆与相关性的小波分析[J],《统计与决策》2007年第6期。
[16]刘凤芹、吴喜之:基于SV模型的深圳股市波动的预测[J],《山西财经大学学报》2004年第26卷第4期。
[17]刘继春:多维GARCH模型的估计和检验[J],《吉林大学学报(自然科学版)》2000年第4期。
[18]刘金全、崔畅:中国沪深股票市场收益率与波动性的实证研究[J],《经济学(季刊)》2002年第3期。
[19]刘金全、郑挺国:我国货币政策冲击对实际产出周期波动的非对称影响分析[J],《数量经济技术经济研究》2006年第10期。
[20]刘金全、郑挺国、隋建利:我国通货膨胀率均值过程和波动过程中的双长记忆性度量与统计检验[J],《管理世界》2007年第7期。
[21]卢志红、郑丕谔:GARCH族模型在上海股市分阶段对比分析中的应用[J],《中国计量学院学报》2004年第1期.
[22]孟利锋、张世英、何信a:具有杠杆效应SV模型的贝叶斯分析及其应用[J],《系统工程》2004年第22卷第3期。
[23]孟利锋、张世英、何信b:SV模型参数估计的经验特征函数方法[J],《系统工程》2004年第22卷第12期。
[24]苏卫东、齐安甜、黄兴:长记忆SV模型的统计性质及其实证分析[J],《系统工程》2004年第22卷第3期。
[25]苏卫东、张世英:随机波动模型估计及在金融风险防范中的应用[J],《天津大学学报》2002年第35卷第3期。
[26]苏卫东、张世英:变截距SV模型及其在上海股市的实证[J],《系统工程理论方法应用》2003年第12卷第1期。
[27]苏卫东、张世英:多元长记忆SV模型及其在沪深股市的应用[J],《管理科学学报》2004年第7卷第1期。
[28]王炳雪、史忠科、阎东明:基于趋势平滑和GARCH的证券市场预测[J],《西安理工大学学报》2002年第18期。
[29]王春峰、蒋祥林、吴晓霖:随机波动性模型的比较分析[J],《系统工程学报》2005年第20卷第2期。
[30]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年第9期。
[31]王宇新:GARCH模型和SV模型对深圳股市的比较[J],《合肥工业大学学报(自然科学版)》2007年第30卷第6期。
[32]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年第22期。
[33]吴长凤:利用回归GARCH模型对我国沪深股市的分析[J],《预测》1999年第4期。
[34]谢赤、吴雄伟:基于Vasicek模型和CIR模型中的中国货币市场利率行为实证分析[J],《中国管理科学》2002年第3期。
[35]徐梅、张世英a:基于小波变换的时变长记忆SV模型估计方法研究[J],《系统工程学报》2006年第21卷第1期。
[36]徐梅、张世英b:基于小波变换的长记忆随机波动模型估计方法研究[J],《中国管理科学》2006年第14卷第1期。
[37]许启发、张世英:Box-Cox-SV模型及其对金融时间序列刻画能力研究[J],《系统工程学报》2005年第20卷第4期。
[38]战雪丽、张世英:基于Copula-SV模型的金融投资组合风险分析[J],《系统管理学报》2007年第16卷第3期。
[39]张瑞锋、张世英:基于VS-MSV模型的金融市场波动溢出分析及实证研究[J],《系统工程》2007年第25卷第8期。
[40]张若东、孙王杰、刘继春:多维门限GARCH模型的平稳遍历性[J],《东北师大学报:自然科学版》2003年第1期。
[41]张世英、柯珂:ARCH模型体系[J],《系统工程学报》2002年第17卷第3期。
[42]赵华:人民币汇率与利率之间的价格和波动溢出效应研究[J],《金融研究》2007年第3期。
[43]赵振全、苏治、丁志国:我国股票市场收益率非对称均值回归特征的计量检验――基于ANST-GARCH模型的实证分析[J],《数量经济技术经济研究》2005年第4期。
[44]周宏山、冀云:非对称随机波动模型在中国股市的应用[J],《统计与信息论坛》2007年第22卷第4期。
[45]周彦、张世英:基于MCMC方法的连续时间SV模型建模研究[J],《工业工程》2007年第10卷第1期。
[46]周彦、张世英、张彤:跳跃连续时间SV模型建模及实证研究[J],《系统管理学报》2007年第16卷第5期。
[47] Aase K K. Contingent claims valuation when the security price is a combination of an Ito?process and a random point process[J]. Stochastic Processes and Their Applications, 1988,28: 185-220.
[48] Abraham B., Balakrishna N., Sivakumar R. Gamma stochastic volatility models[J]. Jour-nal of Forecasting, 2006, 25: 153-171.
[49] Ackerson G A., Fu K S. On state estimation in switching environments[J]. IEEE Trans-actions on Automatic Control, 1970, 15: 10-17.
[50] Aguilar O., West M. Bayesian dynamic factor models and variance matrix discountingfor portfolio allocation[J]. Journal of Business and Economic Statistics, 2000, 18: 338-357.
[51] Ahn D., Gao B. A parametric nonlinear model of term structure dynamics[J]. Review ofFinancial Studies, 1999, 12: 721-762.
[52] A¨?t-Sahalia Y. Nonparametric pricing of interest rate derivatives[J]. Econometrica, 1996a,64: 527-560.
[53] A¨?t-Sahalia Y. Testing continuous-time models of the spot interest rate[J]. Review ofFinancial Studies, 1996b, 9: 385-426.
[54] Akashi H., Kumamoto H. Random sampling approach to state estimation in switchingenvironments[J]. Automatica, 1977, 13: 429-434.
[55] Albert J H., Chib S. Bayes inference via Gibbs sampling of autoregressive time seriessubject to Markov mean and variance shifts[J]. Journal of Business and Economic Statistics,1993, 11: 1-15.
[56] Alexander S S.Price movements in speculative markets: trends or random walks[J]. In-dustrial Management Review, 1961, 2: 7-26.
[57] Alspach D L., Sorenson H W. Nonlinear Bayesian estimation using Gaussian sum ap-proximations[J]. IEEE Transactions on Automatic Control, 1972, 17: 439-448.
[58] Amin K., Jarrow R. Pricing options on risky assets in a stochastic interest rate econ-omy[J]. Mathematical Finance, 1992, 2: 217-237.
[59] Amin K., Ng V. Option valuation with systematic stochastic volatility[J]. Journal ofFinance, 1993, 48: 881-910.
[60] Anderson T G. Stochastic autogregssive volatility: a framework for volatility modeling[J].Mathematical Finance, 1994b, 4: 75-102.
[61] Andersen T G., Bollerslev T. Answering the skeptics: Yes, standard volatility models doprovide accurate forecasts[J]. International Economic Review, 1998, 39: 885-905.
[62] Andersen T G., Bollerslev T., Diebold F X., Labys P. The distribution of exchange ratevolatility[J]. Journal of the American Statistical Association, 2001, 96: 42-55.
[63] Andersen T G., Bollerslev T., Diebold F X., Labys P. Modeling and forecasting realizedvolatility[J]. Econometrica, 2003, 71: 579-625.
[64] Andersen T G., Bollerslev T., Meddahi N. Analytic evaluation of volatility forecasts[J].International Economic Review, 2004, 45: 1079-1110.
[65] Andersen T G., Lund J. Estimating continuous-time stochastic volatility models of theshort-term interest rate[J]. Journal of Econometrics, 1997, 77: 343-377.
[66] Andersen, T G., S?rensen B E. GMM Estimation of a stochastic volatility model: aMonte Carlo study[J]. Journal of Business and Economic Statistics, 1997, 14: 328-352.
[67] Andreou E., Ghysels E. Detecting multiple breaks in financial market volatility dynam-ics[J]. Journal of Applied Econometrics, 2002, 17: 579-600.
[68] Ang A., Bekaert G. Regime switches in interest rates[J]. Journal of Business and Eco-nomic Statistics, 2002, 20: 163-182.
[69] Areal N M P C., Taylor S J. The realized volatility of FTSE-100 futures prices[J]. Journalof Futures Markets, 2002, 22: 627-648.
[70] Asai M. Autoregressive stochastic volatility models with heavy-tailed distributions: Acomparison with multifactor volatility models[J]. Journal of Empirical Finance, 2008, 15:332-341.
[71] Asai M., McAleer M. Dynamic asymmetric leverage in stochastic volatility models[J].Econometric Reviews, 2005, 24: 317-332.
[72] Asai M., McAleer M. Asymmetric multivariate stochastic volatility[J]. Econometric Re-views, 2006, 25: 453-473.
[73] Bachelier L. Theories de la speculation. Ann. Sci. Ecole Norm. Sup, 1900, 17: 21-28.
[74] Bailey W., Stulz E. The pricing of stock index options in a general equilibrium model[J].Journal of Financial and Quantitative Analysis, 1989, 24: 1-12.
[75] Baillie R T., Bollerslev T. The message in daily exchange rates: a conditional-variancetale[J]. Journal of Business and Economic Statistics, 1989, 7: 297-305.
[76] Baillie R T., Bollerslev T., Mikkelson H O. Fractionally integrated generalized autore-gressive conditional heteroskedasticity[J]. Journal of Econometrics, 1996, 74: 3-30.
[77] Bakshi G., Cao C., Chen Z. Empirical performance of alternative options pricing mod-els[J]. Journal of Finance, 1997, 52(5): 2003-2049.
[78] Balduzzi P., Das S., Foresi S., Sundaram, R. A simple approach to threefactor a?ne termstructure models[J]. Journal of Fixed Income, 1996, 6: 43-53.
[79] Balke N., Fomby T B. Shifting trends, segmented trends, and infrequent permanentshocks[J]. Journal of Monetary Economics, 1991, 28: 61-85.
[80] Ball C A., Torous W N. On jumps in common stock prices and their impact on calloption pricing[J]. Journal of Finance, 1985, 40: 155-173.
[81] Ball C A., Torous W N. The stochastic volatility of short-term interest rates: someinternational evidence[J]. Journal of Finance, 1999, 54: 2339-2359.
[82] Bar-Shalom Y., Tse E. Tracking in a cluttered environment with probabilistic data as-sociation[J]. Automatica, 1975, 11: 451-460.
[83] Bardhan I., Chao X. Pricing options on securities with discontinuous returns[J]. Stochas-tic Processes and Their Application, 1993, 48: 123-137.
[84] Barndor?-Nielsen O E., Shephard N. Econometric analysis of realised volatility and itsuse in estimating stochastic volatility models[J]. Journal of the Royal Statistical Society B,2002, 64: 253-280.
[85] Bates D S. The crash of 87: Was it expected? the evidence from option markets[J].Journal of Finance, 1991, 46: 1009-1044.
[86] Bates D S. Jumps and stochastic volatility: exchange rate processes implicit in PHLXDeutschmark options[J]. Review of Financial Studies, 1996b, 9(1): 69-107.
[87] Baum L E., Petrie T. Statistical inference for probabilistic functions of finite state Markovchains[J]. The Annals of Mathematical Statistics, 1966, 37: 1554-1563.
[88] Bauwens L., Laurent S., Rombouts J V K. Multivariate GARCH models: A survey[J].Journal of Applied Econometrics, 2006, 21: 79-109.
[89] Beckers S. A note on estimating the parameters of the di?usion-jump model of stockreturns[J]. Journal of Financial and Quantitative Analysis, 1981, 16(1): 127-140.
[90] Berg A., Meyer R., Yu J. Deviance information criterion for comparing stochastic volatil-ity models[J]. Journal of Business and Economic Statistics, 2004, 22: 107-120.
[91] Bickel P J., Ritov Y., Ryd′en T. Asymptotic normality of the maximum likelhood esti-mator for general hidden Markov models[J]. The Annals of Statistics, 1998, 26: 1614-1635.
[92] Black F., Scholes M. The pricing of options and corporate liabilities[J]. Journal of PoliticalEconomy, 1973, 81: 637-654.
[93] Black F., Derman E., Toy W. A one-factor model of interest rates and its application toTreasury bond options[J]. Financial Analysis Journal, 1990, 46(1): 33-39.
[94] Black F., Karasinski P. Bond and option pricing when short rates are lognormal[J].Financial Analysts Journal, 1991, 47(4):52-59.
[95] Blair B J., Poon S H., Taylor S J. Forecasting S&P 100 volatility: The incrementalinformation content of implied volatilities and high frequency index returns[J]. Journal ofEconometrics, 2001, 105: 5-16.
[96] Bliss R R., Smith D C. The elasticity of interest rate volatility: Chan, Karolyi, Longsta?,and Sanders revisited[J]. Journal of Risk, 1998, 1(1): 21-46.
[97] Blom H., Bar-Shalom Y. The interacting multiple model algorithm for systems withMarkovian switching coe?cients[J]. IEEE Transactions on Automatic Control, 1988, 33:780-783.
[98] Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Eco-nomics, 1986, 31: 307-327.
[99] Bollerslev T. Modelling the coherence in short-run nominal exchange rates: A multivari-ate generalized ARCH approach[J]. Review of Economics and Statistics, 1990, 72: 498-505.
[100] Bollerslev T. A Conditionally Heteroskedastic Time Series Model for Speculative Pricesand Rates of Return[J]. Review of Economics and Statistics, 1987, 69: 542-47.
[101] Bollerslev T., Chou R Y., Kroner K F. ARCH modeling in finance[J]. Journal of Econo-metrics, 1992, 52: 5-59.
[102] Bollerslev T., Engle R F., Wooldridge J. A capital asset pricing model with time varyingcovariances[J]. Journal of Political Economy, 1988, 96: 116-131.
[103] Brailsford T J., Maheswaran K. The dynamics of the Australian short-term interestrate[J]. Australian Journal of Management, 1998, 23: 213-234.
[104] Breidt F J., Crato N., de Lima P J F. The detection and estimation of longmemory instochastic volatility[J]. Journal of Econometrics, 1998, 83: 325-348.
[105] Brennan M J. The pricing of contingent claims in discrete time models[J]. Journal ofFinance, 1979, 34: 53-68.
[106] Brennan M J., Schwartz E S. Savings bonds, retractable bonds and callable bonds[J].Journal of Financial Economics, 1977, 5: 67-88.
[107] Brennan M J., Schwartz E. A continuous-time approach to the pricing of bonds[J].Journal of Banking and Finance, 1979, 3: 133-155.
[108] Brennan M J., Schwartz E S. Analyzing convertible bonds[J]. Journal of Financial andQuantitative Analysis, 1980, 15(4): 907-929.
[109] Brennan M J., Schwartz E S. An Equilibrium Model of Bond Pricing and a Test ofMarket E?ciency[J]. Journal of Financial and Quantitative Analysis, 1982, 17(3): 301-329.
[110] Brenner R J., Harjes R H., Kroner K F. Another look at models of the short-term interestrate[J]. Journal of Financial and Quantitative Analysis, 1996, 31(1): 85-107.
[111] Brown S J., Dybvig P H. Empirical implications of the Cox, Ingersoll, Ross theory ofthe term structure of interest rates[J]. Journal of Finance, 1986, 41: 143-172.
[112] Byers S L., Nowman K B. Forecasting UK and US interest rates using continuous timeterm structure models[J]. International Review of Financial Analysis, 1998, 7: 191-206.
[113] Cai J. A Markov model of switching-regime ARCH[J]. Journal of Business and EconomicStatistics, 1994,12: 309-316.
[114] Carter C K., Kohn R. On Gibbs sampling for state space models[J]. Biometrika, 1994,81: 541-553.
[115] Carter C., Kohn R. Semiparametric Bayesian inference for time series with mixed spec-tra[J]. Journal of the Royal Statistical Society B, 1997, 255-268.
[116] Carvalho C M. and Lopes H F. Simulation-based sequential analysis of Markov switchingstochastic volatility models[J]. Computational Statistics and Data Analysis, 2007, 51: 4526-4542.
[117] Cavaliere G. Asymptotics for unit root tests under Markov regime-switching[J]. Econo-metrics Journal, 2003, 6: 193-216.
[118] Chan K., Karolyi G., Longsta? F., Sanders A. An empirical comparison of alternativemodels of the short-term interest rate[J]. Journal of Finance, 1992a, 47(3): 1209-1227.
[119] Chan K., Karolyi G., Longsta? F., Sanders A. The volatility of Japanese interest rates: Acomparison of alternative term structure models[J]. Pacific-Basin Capital Markets Research,1992b, 3: 119-136.
[120] Chapman D A., Pearson N D. Recent advances in estimating term structure models[J].Financial Analysts Journal, 2001, 57(3): 77-95.
[121] Chen L. Stochastic mean and stochastic volatility three-factor model of the term struc-ture of interest rates and its applications in derivatives pricing and risk management[J].Financial Markets, Institutions and Instruments, 1996, 5(1): 1-18.
[122] Chen R R., Scott L. Pricing interest rate options in a two-factor Cox-Ingersoll-Rossmodel of the term structure[J]. Review of Financial Studies, 1992, 5: 613-636.
[123] Chernov M., Gallant A R., Ghysels E., Tauchen G. Alternative models for stock pricedynamics[J]. Journal of Econometrics, 2003, 116: 225-257.
[124] Chesney M., Scott L O. Pricing European currency options: a comparison of the modifiedBlack-Scholes model and a random variance model[J]. Journal of Financial QuantitativeAnalysis, 1989, 24: 267-284.
[125] Chib S. Bayes estimation of regressions with autoregressive errors: a Gibbs samplingapproach[J]. Journal of Econometrics, 1993, 58: 275-294.
[126] Chib S. Calculating posterior distributions and modal estimates in Markov mixturemodels[J]. Journal of Econometrics, 1996, 75: 79-97.
[127] Chib S., Nardari F., Shephard N. Markov chain Monte Carlo methods for generalizedstochastic volatility models[J]. Journal of Econometrics, 2002, 108: 281-316.
[128] Chib S., Nardari F., Shephard N. Analysis of high-dimensional multivariate stochasticvolatility models[J]. Journal of Econometrics, 2006, 134: 341-371.
[129] Chow G C. Tests of equality between sets of coe?cients in two linear linear regressions(Ref: 74V42 p601-608)[J]. Econometrica, 1960, 28: 591-605.
[130] Chow H K. Robust estimation in time series: an approximation to the Gaussian sumfilter[J]. Communications in Statistics - Theory and Methods, 1994, 23: 3491-3505.
[131] Clark P K. A subordinated stochastic process model with fixed variance for speculativeprices[J]. Econometrica , 1973,41: 135-156.
[132] Conley T G., Hansen L P., Luttmer E G J., Scheinkman J A. Short-term interest ratesas subordinated di?usions[J]. Review of Financial Studies, 1997, 10(3): 525-577.
[133] Constantinides G. A theory of the nominal term structure of interest rates[J]. Review ofFinancial Studies, 1992, 5: 531-552.
[134] Cosslett S R., Lee L F. Serial correlation in latent discrete variable models[J]. Journalof Econometrics, 1985, 27: 79-97.
[135] Cox J C., Ross S A. The valuation of options for alternative stochastic processes[J].Journal of Financial Economics, 1976, 3: 145-166.
[136] Cox J C., Ingersoll J., Ross S A. An analysis of variable rate loan contracts[J]. Journalof Finance, 1980, 35: 389-403.
[137] Cox J C., Ingersoll J., Ross S A. A theory of the term structure of interest rates[J].Econometrica, 1985, 53(2): 385-407.
[138] Dahlquist M. On alternative interest rate processes[J]. Journal of Banking and Finance,1996, 20: 1093-1119.
[139] Dalang R., Morton A. and Willinger W. Equivalent martingale measures and no arbitragein stochastic security market models[J], Stochastics and Stochastic Reports,1989, 29: 185-202.
[140] Dai Q., Singleton K J. Specification analysis of a?ne term structure models[J]. Journalof Finance, 2001, 55: 1943-1978.
[141] Danielsson J. Stochastic volatility in asset prices: Estimation with simulated maximumlikelihood[J]. Journal of Econometrics, 1994, 61: 375-400.
[142] Danielsson J. Multivariate stochastic volatility models: estimation and a comparisonwith VGARCH models[J]. Journal of Empirical Finance, 1998, 5: 155-173.
[143] Danielsson J., Richard J F. Accelerated Gaussian importance sampler with applicationto dynamic latent variable models[J]. Journal of Applied Econometrics, 1993, 8: 153-173.
[144] Das S R. The surprise element: Jumps in interest rates[J]. Journal of Econometrics,2002, 106: 27-65.
[145] de Jong P., Shephard N. The simulation smoother for time series models[J]. Biometrika,1995, 82: 339-350.
[146] Derman E., Kani I. Riding on a smile[J]. Risk, 1994, 7: 32-39.
[147] Derman E., Ergener D., Kani I. Static options replication[J]. Journal of Derivatives,1995, 2: 78-95.
[148] Dickey D A., Fuller W A. Likelihood ratio statistics for autoregressive time series witha unit root[J]. Econometrica , 1981, 49: 1057-1072.
[149] Diebold F X. Modeling the persistence of conditional variances: A comment[J]. Econo-metric Reviews, 1986, 5: 51-56.
[150] Diebold F X., Nerlove M. The dynamics of exchange rate volatility: a multivariate latentfactor GARCH model[J]. Journal of Applied Econometrics, 1989, 4: 1-21.
[151] Ding Z., Granger C W J., Engle R F. A long memory property of stock market returnsand a new model[J]. Journal of Empirical Finance, 1993, 1: 83-108.
[152] Dothan U. On the term structure of interest rates[J]. Journal of Financial Economics,1978, 7: 229-264.
[153] Du?e D., Kan R. A yield-factor model of interest rates[J]. Mathematical Finance, 1996,6: 379-406.
[154] Du?e D., Singleton K J. Simulated moments estimation of Markov models of assetprices[J]. Econometrica, 1993, 61: 929-952.
[155] Dupire B. Pricing with a smile[J]. Rsik, 1994, 7: 18-20.
[156] Durbin J., Koopman S J. Time series analysis of non-Gaussian observations based onstate space models from both classical and Bayesian perspectives (with discussion)[J]. Jour-nal of the Royal Statistical Society B, 2000, 62: 3-56.
[157] Durham G B. Likelihood-based specification analysis of continuous-time models of theshort-term interest rates[J]. Journal of Financial Economics, 2003, 70(3): 463-487.
[158] Durham G B. Monte Carlo methods for estimating, smoothing, and filtering one- andtwo-factor stochastic volatility models[J]. Journal of Econometrics, 2005, 133: 273-305.
[159] Dueker M. Markov switching in GARCH processes and meanreverting stock-marketvolatility[J]. Journal of Business and Economic Statistics, 1997, 15: 26-34.
[160] Durbin J., Koopman S J. Monte Carlo maximum likelihood estimation for non-Gaussianstate space models[J]. Biometrika, 1997, 84: 669-684.
[161] Engel C., Hamilton J D. Long swings in the Dollar: Are they in the data and do marketsknow it? [J].The American Economic Review, 1990, 80: 689-713.
[162] Engle R F. Autoregressive conditional heteroscedasticity with estimates of the varianceof United Kingdom in?ation[J]. Econometrica, 1982, 50: 987-1007.
[163] Engle R F., Kroner K F. Multivariate simultaneous generalized ARCH[J]. EconometricTheory, 1995, 11: 122-50.
[164] Engle R F., Lilien D M., Robins R P. Estimating time varying term premis in the termstructure: the ARCH-M model[J]. Econometrica, 1987, 55(2): 391-407.
[165] Engle R F., Ng V K. Measuring and testing the impact of news on volatility[J]. Journalof Finance , 1993, 48: 1749-1801.
[166] Eraker B. MCMC analysis of di?usion models with application to finance[J]. Journal ofBusiness and Economic Statistics, 2001, 19: 177-191.
[167] Fama E F. The stable paretian distribution[J]. Journal of Business, 1963, 36: 420-429.
[168] Fama E F. The behavior of stock market prices[J]. Journal of Business, 1965, 38: 34-105.
[169] Filardo A J. Business-cycle phases and their transitional dynamics[J]. Journal of Busi-ness and Economic Statistics, 1994, 12: 299-308.
[170] Filardo A J., Gordon S F. Business cycle duration[J]. Journal of Econometrics, 1998,85: 99-123.
[171] Fiorentini G., Leo′n A., Rubio G. Estimation and empirical performance of Heston’sstochastic volatility model: The case of a thinly traded market[J]. Journal of EmpiricalFinance, 2002, 9: 225-255.
[172] Fleming J., Kirby C., Ostdiek B. Information and volatility linkages in the stock, bondand money markets[J]. Journal of Financial Economics, 1998, 49:111-137.
[173] Fong H G., Vasicek O A. Fixed Income Volatility Management[J]. The Journal of Port-folio Management, 1991, 17(4): 41-46.
[174] Fornari F., Mele A. Modeling the changing asymmetry of conditional variances[J]. Eco-nomics Letters, 1996, 50: 197-203.
[175] Fornari F., Mele A. Sign- and volatility-switching ARCH models: theory and applicationsto international stock markets[J]. Journal of Applied Econometrics, 1997, 12: 49-65.
[176] Francq C., Roussignol M., Zakoian J. Conditional heteroscedasticity driven by hiddenMarkov chains[J]. Journal of Time Series Analysis, 2001, 22: 197-220.
[177] French K R., Schwert G W., Stambaugh R F. Expected Stock Returns and Volatility[J].Journal of Financial Economics, 1987, 19: 3-29.
[178] Fridman M., Harris L. A Maximum Likelihood Approach for Non-Gaussian StochasticVolatility Models[J]. Journal of Business and Economic Statistics, 1998, 16: 284-291.
[179] Fru¨hwirth-Schnatter S., Kaufmann S. Model-based clustering of multiple time series[J].Journal of Business and Economic Statistics, 2008, 26(1): 78-89.
[180] Gallant A R., Tauchen G E. Which moments to match?[J]. Econometric Theory, 1996,12: 657-681.
[181] Gallant A R., Tauchen G E. Reprojecting partially observed systems with application tointerest rate di?usions[J]. Journal of the American Statistical Association, 1998, 93: 10-24.
[182] Gelfand A E., Smith A F M., Lee T M. Bayesian Analysis of constrained parametersand truncated data problems using Gibbs Sampling[J]. Journal of the American StatisticalAssociation, 1992, 87: 523-532.
[183] Geman S., Geman D. Stochastic relaxation, Gibbs distributions and the Bayesian restora-tion of images[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984,6: 721-741.
[184] Geweke J F. Bayesian inference in econometric models using Monte Carlo integration[J].Econometrica, 1989, 57: 1317-1339.
[185] Geweke J F. Using simulation methods for Bayesian econometric models: inference,development and communication[J]. Econometric Reviews, 1999, 18: 1-127.
[186] Gibbons M R., Rarnaswamy K. A test of the Cox, Ingersoll and Ross model of the termstructure[J]. Review of Financial Studies, 1993, 6: 619-658.
[187] Glosten L R., Jagannathan R., Runkle D E. On the relation between the expected valueand the volatility of the nominal excess return on stocks[J]. Journal of Finance, 1993, 48:1779-1801.
[188] Goldfeld S., Quandt R. A Markov model for switching regression[J]. Journal of Econo-metrics, 1973, 1: 3-16.
[189] Gordon K., Smith A F M. Modeling and monitoring biomedical time series[J]. Journalof the American Statistical Association, 1990, 85: 328-337.
[190] Gordon N., Salmond D., Smith A. A Novel Approach to Non-linear and Non-GaussianBayesian State Estimation[J]. IEE Proceedings, 1993, 140: 107-133.
[191] Gouri′eroux C.,Monfort A., Renault E. Indirect inference[J]. Journal of Applied Econo-metrics, 1993, 8: 85-118.
[192] Granger C W J., Hyung N. Occasional structural breaks and long memory with anapplication to the S&P500 absolute stock returns[J]. Journal of Empirical Finance, 2004,11: 399-421.
[193] Granger C W J., Morris M. Time series modeling and interpretation[J]. Journal of theRoyal Statistical Society A, 1976, 139: 246-257.
[194] Gray S F. Modeling the conditional distribution of interest rates as a regime-switchingprocess[J]. Journal of Financial Economics, 1996, 42: 27-62.
[195] Hall S G., Psaradakis Z., Sola M. Cointegration and changes in regime: The Japaneseconsumption function. Journal of Applied Econometrics, 1997, 12: 151-168.
[196] Hall S G., Psaradakis Z., Sola M. Detecting periodically collapsing bubbles: A Markov-switching unit root test[J]. Journal of Applied Econometrics, 1999, 14: 143-154.
[197] Hamilton J D. Rational expectations econometric analysis of changes in regime: Aninvestigation on the term structure of interest rates[J]. Journal of Economic Dynamics andControl, 1988, 12: 385-423.
[198] Hamilton J D. A New Approach to the Economic Analysis of Nonstationary Time Seriesand the Business Cycle[J]. Econometrica, 1989, 57(2): 357-384.
[199] Hamilton J D., Lin G. Stock market volatility and the business cycle[J]. Journal ofApplied Econometrics, 1996, 11: 573-593.
[200] Hamilton J D., Susmel R. Autoregressive conditional heteroscedasticity and changes inregime[J]. Journal of Econometrics, 1994, 64: 307-333.
[201] Hamilton J D. Specification testing in Markov-switching time-series models[J]. Journalof Econometrics, 1996, 70: 127-157.
[202] Hansen L P. Large sample properties of generalized method of moments estimators[J].Econometrica, 1982, 50: 1029-1054.
[203] Harrison M., Kreps D. Martingale and arbitrage in multiperiod securities markets[J].Journal of Economic Theory, 1979, 20: 381-408.
[204] Harrison P J., Stevens C F. Bayesian Forecasting[J]. Journal of the Royal StatisticalSociety Series B, 1976, 38: 205-247.
[205] Harvey A., Ruiz E., Shephard N. Multivariate stochastic variance models[J]. Review ofEconomic Studies, 1994, 61: 247-264.
[206] Harvey A C., Shephard N. The estimation of an asymmetric stochastic volatility modelfor asset returns[J]. Journal of Business and Economic Statistics, 1996, 14: 429-434.
[207] Heston S I. A closed form solution for options with stochastic volatility with applicationsto bond and currency options[J]. Review of Financial Studies, 1993, 6: 327-344.
[208] Hiraki T., Takezawa N. How sensitive is short-term Japanese interest rate volatility tothe level of the interest rate?[J]. Economics Letters, 1997, 56: 325-332.
[209] Hogan M. Problems in certain two-factor term structure models[J]. Annals of AppliedProbability, 1993, 3: 576-581.
[210] Holst U., Lindgren G., Holst J., Thuvesholmen M. Recursive estimation in switchingautoregressions with a Markov regime[J]. Journal of Time Series Analysis, 1994, 15: 489-506.
[211] Hong Y., Li H., Zhao F. Out-of-sample performance of discrete-time spot interest ratemodels[J]. Journal of Business and Economic Statistics, 2004, 22: 457-473.
[212] Hsieh D A. Modeling heteroskedasticity in daily foreign exchange rates. Journal of Busi-ness and Economic Statistics, 1989, 7: 307-317.
[213] Hsieh D A. Chaos and nonlinear dynamics: application to financial markets[J]. Journalof Finance, 1991, 46: 1839-1877.
[214] Hull J., White A. The pricing of options on assets with stochastic volatilities[J]. Journalof Finance, 1987, 42: 281-300.
[215] Hull J C., White A. Pricing interest-rate derivative securities[J]. The Review of FinancialStudies, 1990, 3(4): 573-592.
[216] Hull J C., White A. One-factor interest-rate models and the valuation of interest-ratederivative securities[J]. Journal of Financial and Quantitative Analysis, 1993, 28: 235-254.
[217] Hull J., White A. Numerical procedures for implementing term structure models I: single-factor Models[J]. Journal of Derivatives, 1994, 2, 7-16.
[218] Hwang S., Valls P. Small sample properties of GARCH estimates and persistence[J].European Journal of Finance, 2006, 12: 473-494.
[219] Hwang S., Satchell S E., Valls P. How persistent is stock return volatility? An answerwith Markov regime switching stochastic volatility models[J]. Journal of Business Financeand Accounting, 2007, 34: 1002-1024.
[220] Jacquier E., Polson N G., Rossi P E. Bayesian analysis of stochastic volatility models(with discussion)[J]. Journal of Business and Economic Statistics, 1994, 12: 371-417.
[221] Jacquier E., Polson N G., Rossi P E. Bayesian analysis of stochastic volatility modelswith fat-tails and correlated errors[J]. Journal of Econometrics, 2004, 122: 185-212.
[222] Jamshidian F. A simple class of square-root interest-rate models. Applied MathematicalFinance, 1995, 2: 61-72.
[223] Jeanblanc-Picqu′e M., Pontier M. Optimal portfolio for a small investor in a market withdiscontinuous prices[J]. Applied Mathematical Optimisation, 1990, 22: 287-310.
[224] Jiang G. Stochastic volatility and jump-di?usion-implications on option pricing[J]. In-ternational Journal of Theoretical and Applied Finance, 1999, 2: 409-440.
[225] Johnson H., Shanno D. Option pricing when the variance is changing[J]. Journal ofFinancial and Quantitative Analysis, 1987, 22: 143-152.
[226] Kalimipalli M., Susmel R. Regime-Switching stochastic volatility and short-term interestrates[J]. Journal of Empirical Finance, 2004, 11: 309-329.
[227] Karlsen H A., Tj?theim D. Autoregressive segmentation of signal traces with applica-tion to geological dipmeter measurements[J]. IEEE Transactions on Geoscience and RemoteSensing, 1990, 28: 171-181.
[228] Kaufmann S., Fru¨hwirth-Schnatter S. Bayesian analysis of switching ARCH models[J].Journal of Time Series Analysis, 2002, 23: 425-458.
[229] Kawakatsu H. Numerical integration-based Gaussian mixture filters for maximum likeli-hood estimation of asymmetric stochastic volatility models[J]. Econometrics Journal, 2007,10: 342-358.
[230] Kim C J. Sources of monetary growth uncertainty and economic activity: The time-varying parameter model with heteroscedastic disturbances[J]. The Review of Economicsand Statistics, 1993a, 75: 483-492.
[231] Kim C J. Unobserved-component time series models with Markovswitching heteroscedas-ticity: Changes in regime and the link between in?ation rates and in?ation uncertainty[J].Journal of Business and Economic Statistics, 1993b, 11: 341-349.
[232] Kim C J. Dynamic Linear Models with Markov-Switching[J]. Journal of Econometrics,1994, 60: 1-22.
[233] Kim D., Kon S J. Structural change and time dependence in models of stock returns[J].Journal of Empirical Finance, 1999, 6: 283-308.
[234] Kim I M. A dynamic programming approach to the estimation of Markov switchingregression models[J]. Journal of Statistical Computation and Simulation, 1993c, 45: 61-76.
[235] Kim S., Shephard N., Chib S. Stochastic Volatility: Likelihood Inference and Comparisonwith ARCH Models[J]. Review of Economic Studies, 1998, 65: 361-393.
[236] Kitagawa G. Non-Gaussian State Space Modeling of Nonstationary Time Series (withdiscussion)[J]. Journal of the American Statistical Association, 1987, 82: 1032-1063.
[237] Kitagawa G. Monte Carlo Filter and Smoother for Non-Gaussian Non-linear State SpaceNodels[J]. Journal of Computational and Graphical Statistics, 1996, 5: 1-25.
[238] Klaasen F. Improving GARCH volatility forecasts with regime-switching GARCH[J].Empirical Economics, 2002, 27: 363-394.
[239] Knight J L., Yu J. The empirical characteristic function in time series estimation[J].Econometric Theory, 2002, 18: 691-721.
[240] Knight J L., Satchell S E., Yu J. Estimation of the stochastic volatility model by the em-pirical characteristic function method[J]. Australian and New Zealand Journal of Statistics,2002, 44: 319-335.
[241] Koedijk K G., Nissen F G J A., Scotchman P C., Wol? C C P. The dynamics of short-term interest rate volatility reconsidered[J]. European Finance Review, 1997, 1: 105-130.
[242] Koopman S J., Uspensky E H. The stochastic volatility in mean model - empiricalevidence from international stock markets[J]. Journal of Applied Econometrics, 2002, 17:667-689.
[243] Krolzig H M. Business cycle measurement in the presence of structural change: Interna-tional evidence[J]. International Journal of Forecasting, 2001, 17: 349-368.
[244] Krolzig H M., Sensier M. A disaggregated Markov-switching model of the business cyclein UK manufacturing[J]. The Manchester School, 2000, 68: 442-460.
[245] Lam P S. The Hamilton model with a general autoregressive component: Estimation andcomparison with other models of economic time series[J]. Journal of Monetary Economics,1990, 26: 409-432.
[246] Lamoureux C G., Lastrapes W D. Persistence in variance, structural change, and theGARCH model[J]. Journal of Business and Economic Statistics, 1990, 8: 225-234.
[247] Lastrapes W D. Exchange rate volatility and U.S. monetary policy: an ARCH applica-tion[J]. Journal of Money, Credit and Banking, 1989, 21: 66-77.
[248] Leroux B G. Maximum-likelihood estimation for hidden Markov models[J]. StochasticProcesses and Their Applications, 1992, 40: 127-143.
[249] Leybourne S J., Mills T C., Newbold P. Spurious rejections by Dickey-Fuller tests in thepresence of a break under the null[J]. Journal of Econometrics, 1998, 87: 191-203.
[250] Liesenfeld R., Jung R C. Stochastic volatility models: conditional normality versusheavy-tailed distributions[J]. Journal of Applied Econometrics, 2000, 15: 137- 160.
[251] Liesenfeld R., Richard J F. Univariate and multivariate stochastic volatility models:estimation and diagnostics[J]. Journal of Empirical Finance, 2003, 10: 505-531.
[252] Lin D K., Guttman I. Handling spuriosity in the Kalman filter[J]. Statistics and Proba-bility Letters, 1993, 16: 259-268.
[253] Lindgren G. Markov regime models for mixed distributions and switching regressions[J].Scandinavian Journal of Statistics, 1978, 5: 81-91.
[254] Lintner J. The valuation of risky assets, the selection of risky investment in stock port-folios, capital budgets[J]. Review of Economics, Statistics, 1965, 47: 13-37.
[255] Litterman R, Scheinkman J. Common factors a?ecting bond returns[J]. Journal of FixedIncome, 1991, 1: 54-61.
[256] Litterman R., Scheinkman J., Weiss L. Volatility and the Yield Curve[J]. The Journalof Fixed Income,1991, 1: 49-53.
[257] Lo A. Maximum likelihood estimation of generalized Ito? processes with discretely sam-pled data[J]. Econometric Theory, 1988, 4: 231-247.
[258] Longsta? F A. A nonlinear general equilibrium model of the term structure of interestrates[J]. Journal of Financial Economics, 1989, 23: 195-224.
[259] Longsta? F A., Schwartz E S. Interest rate volatility and the term structure: A two-factor general equilibrium model[J]. Journal of Finance, 1992, 47: 1259-1282.
[260] Lumsdaine R L., Papell D H. Multiple trend breaks and the unit root hypothesis[J]. TheReview of Economics and Statistics, 1997, 79: 212-218.
[261] Mahieu R., Schotman P. An empirical application of stochastic volatility models[J].Journal of Applied Econometrics, 1998, 13: 333-360.
[262] Mandelbrot B B. The variation of certain speculative prices[J]. Journal of Business,1963, 36: 394-416.
[263] Markowitz M H. Portfolio selection[J]. Journal of F inance , 1952, 7(1): 77-91.
[264] McCulloch R E., Tsay R S. Bayesian inference of trend- and di?erence-stationarity[J].Econometric Theory, 1994a, 10: 596-608.
[265] McCulloch R E., Tsay R S. Statistical analysis of economic time series via Markovswitching models[J]. Journal of Time Series Analysis, 1994, 15: 523-539.
[266] Melino A., Turnbull S M. Pricing foreign currency options with stochastic volatility[J].Journal of Econometrics, 1990, 45: 239-265.
[267] Merton R C. The theory of rational option pricing[J]. Bell Journal of Economics, 1973,4(1): 141- 183.
[268] Merton R C. Option pricing when underlying stock returns are discontinuous[J]. Journalof Financial Economics, 1976, 3: 125-144.
[269] Merton R C. On estimating the expected return on the market: An exploratory investi-gation[J]. Journal of Financial Economics, 1980, 8: 323-361.
[270] Meyer R., Yu J. BUGS for a Bayesian analysis of stochastic volatility models[J]. Econo-metrics Journal, 2000, 3: 198-215.
[271] Mikosch T., Starica C. Nonstationarities in financial time series, the long-range depen-dence, and the IGARCH e?ects[J]. Review of Economics and Statistics, 2004, 86: 378-390.
[272] Mossin J. Equilibrium in a capital asset market[J]. Econometrica, 1966, 34: 768-783.
[273] Naik V. Option valuation and hedging strategies with jumps in the volatility of assetreturns[J]. Journal of Finance, 1993, 48: 1969-1984.
[274] Nakajima J., Omori Y. Leverage, heavy-tails and correlated jumps in stochastic volatilitymodels[J]. Computational Statistics and Data Analysis, 2008, doi:10.1016/j.csda.2008.03.015.
[275] Neftci S N. Are economic time series asymmetric over the business cycle?[J]. Journal ofPolitical Economy, 1984, 92: 307-328.
[276] Nelson D B. Stationarity and persistence in the GARCH(1,1) model[J]. EconometricTheory, 1990a, 6: 318-334.
[277] Nelson D B. ARCH models as di?usion approximations[J]. Journal of Econometrics,1990b, 45: 7-38.
[278] Nelson D B. Conditional heteroskedasticity in asset returns: a new approach[J]. Econo-metrica, 1991, 59: 347-370.
[279] Nelson C R., Piger J., Zivot E. Markov regime switching and unit-root tests[J]. Journalof Business and Economic Statistics, 2001, 19: 404-415.
[280] Nowman K B. Gaussian estimation of single-factor continuous time models of the termstructure of interest rates[J]. Journal of Finance, 1997, 52(4): 1695-1706.
[281] Nowman K B. Continuous-time short term interest rate models[J]. Applied FinancialEconomics, 1998, 8: 401-407.
[282] Nowman K B. The volatility of Japanese interest rates: Evidence for certificate of depositand gensaki rates[J]. International Review of Financial Analysis, 2002, 11: 29-38.
[283] Omori Y., Chib S., Shephard N., Nakajima J. Stochastic volatility with leverage: fastand e?cient likelihood inference[J]. Journal of Econometrics, 2007, 140: 425-449.
[284] Pagan A R., Schwert G W. Alternative models for conditional stock volatility[J]. Journalof Econometrics, 1990, 45: 267-290.
[285] Pearson N D., Sun T S. Exploiting the conditional density in estimating the term struc-ture: an application to the Cox, Ingersoll and Ross model[J]. Journal of Finance, 1994, 49:1279-1304.
[286] Pennacchi G G. Identifying the dynamics of real interest rates and inf lation: Evidenceusing survey data[J]. Review of Financial Studies, 1991, 4: 53-86.
[287] Perron P. The great crash, the oil price shock, and the unit root hypothesis[J]. Econo-metrica, 1989, 57: 1361-401.
[288] Petrie T. Probabilistic functions of finite state Markov chains[J]. The Annals of Mathe-matical Statistics, 1969, 40: 97-115.
[289] Phillips K L. A two-country model of stochastic output with changes in regime[J]. Journalof International Economics, 1991, 31: 121-142.
[290] Pitt M., Shephard N. Filtering via Simulation: Auxiliary Particle Filter[J]. Journal ofthe American Statistical Association, 1999, 94: 590-599.
[291] Poon S H., Taylor S. Macroeconomic factors and the UK stock market[J]. Journal ofBusiness, Finance and Accounting, 1991, 18(5): 619-636.
[292] Poon S H., Granger C W J. Forecasting volatility in financial markets: a review[J].Journal of Economic Literature, 2003, 41: 478-539.
[293] Press J. A compound events model for security prices[J]. Journal of Business, 1967, 40:317-335.
[294] Psaradakis Z. Markov-level shifts and the unit-root hypothesis[J]. The EconometricsJournal, 2001, 4: 225-241.
[295] Psaradakis Z. On the asymptotic behaviour of unit root tests in the presence of a Markovtrend[J]. Statistics & Probability Letters, 2002, 57: 101-109.
[296] Quandt R E. A new approach to estimating switching regressions[J]. Journal of theAmerican Statistical Association, 1972, 67: 306-310.
[297] Rabiner L R. A tutorial on hidden Markov models and selected applications in speechrecognition[J]. Proceedings of the IEEE, 1989, 77, 257-286.
[298] Ray B K., Tsay R S. Long-range dependence in daily stock volatilities[J]. Journal ofBusiness and Economic Statistics, 2000, 18: 254-262.
[299] Richard S F. An arbitrage model of the term structure of interest rates[J]. Journal ofFinancial Economics, 1978, 6: 33-57.
[300] Rogers L C G. Gaussian errors[J]. Risk, 1996, 9(1): 42-45.
[301] Ross S A. The arbitrage theory of capital asset pricing[J]. Journal of Economic Theory,1976, 13: 341-360.
[302] Rubinstein M. The valuation of uncertain income streams and the pricing of options[J].Bell Journal of Economics, 1976, 7: 407-425.
[303] Rubinstein M. Implied binomial trees[J]. Journal of Finance, 1994, 69: 771-818.
[304] Ruiz E. Quasi-maximum likelihood estimation of stochastic volatility models[J]. Journalof Econometrics, 1994, 63: 289-306.
[305] Samuelson P. Rational theory of warrant pricing[J]. Industrial Management Review, 1965,6: 13-32.
[306] Sandmann K. The pricing of options with an uncertain interest rate: a discrete-timeapproach[J]. Mathematical Finance, 1993, 3: 201-216.
[307] Sandmann K., Sondermann D. A term structure model and the pricing of interest ratederivatives[J]. Review of Futures Markets, 1993, 12(2): 391-423.
[308] Sandmann K., Sondermann D. On the stability of log-normal interest rate models andthe pricing of Eurodollar futures[J]. Mathematical Finance, 1997, 7(2): 119-125.
[309] Sandmann G., Koopman S J. Estimation of stochastic volatility models via Monte Carlomaximum likelihood[J]. Journal of Econometrics, 1998, 87: 271-301.
[310] Sclove S L. Time series segmentation: A model and a method[J]. Information Science,1983, 29: 7-25.
[311] Scott L. Option pricing when the variance changes randomly: theory, estimators, andapplications[J]. Journal of Financial and Quantitative Analysis, 1987, 22: 419-438.
[312] Scott L. Pricing stock options in a jump-di?usion model with stochastic volatility andinterest rates: Applications of fourier inversion methods[J]. Mathematical Finance, 1997, 7:413-426.
[313] Sharpe W. Capital asset prices:a theory of market equilibrium under conditions of risk[J].Journal of Finance, 1964, 19: 425-442.
[314] Shephard N G. Fitting non-linear time series models, with application to stochasticvariance models[J]. Journal of Applied Econometrics, 1993, 8: 135-152.
[315] Shepard N. Partial non-Gaussian state space[J]. Biometrika, 1994, 81: 115-131.
[316] Shephard N G. Discussion of Durbin and Koopman[J]. Journal of the Royal StatisticalSociety, Series B, 2000, 62, 30-32.
[317] Shephard N G., Kim S. Comment on E. Jacquier, N. Polson and E. Rossi [J]. Journal ofBusiness and Economic Statistics, 1994, 12: 406-410.
[318] Shephard N G., Pitt M K. Likelihood analysis of non-Gaussian measurement time se-ries[J]. Biometrika, 1997, 84: 653-667.
[319] Shumway R H., Sto?er D S. Dynamic linear models with switching[J]. Journal of theAmerican Statistical Association, 1991, 86: 763-769.
[320] Singleton K J. Estimation of a?ne asset pricing models using the empirical characteristicfunction[J]. Journal of Econometrics, 2001, 102: 111-141.
[321] van der Sluis P J. Emmpack 1.01: C/C++ code for use with Ox for estimation ofunivariate stochastic volatility models with the e?cient method of moments[J]. Studies inNonlinear Dynamics and Econometrics, 1997, 2(3): 77-94.
[322] Smith D R. Markov-Switching and stochastic volatility di?usion models of short-terminterest rates[J]. Journal of Business and Economic Statistics, 2002, 20: 183-197.
[323] Smith A F M., Gelfand A E. Bayesian statistics without tears: a samplingresamplingperspective[J]. American Statistican, 1992, 46:84-88.
[324] Smith A F M., Roberts G O. Bayesian computation via the Gibbs sampler and relatedMarkov chain Monte Carlo methods[J]. Journal of the Royal Statistical society, 1993, 55:3-23.
[325] Smith A F M., West M. Monitoring renal transplants: An application of the multiprocessKalman filter[J]. Biometrics, 1983, 39: 867-878.
[326] So M K P., Choi C Y. A multivariate threshold stochastic volatility model[J]. Mathe-matics and Computers in Simulation, 2008, doi:10.1016/j.matcom.2007.12.003.
[327] So M K P., Lam K., Li W K. Multivariate modelling of the autoregressive randomvariance process[J]. Journal of Time Series Analysis, 1997, 18(4): 429-446.
[328] So M K P., Lam K., Li W K. A stochastic volatility model with Markov switching[J].Journal of Business and Economic Statistics, 1998, 16: 244-253.
[329] So M K P., Li W K. Bayesian unit root testing in stochastic volatility models[J]. Journalof Business and Economic Statistics, 1999, 17: 491-496.
[330] So M K P., Li W K., Lam K. A threshold stochastic volatility model[J]. Journal ofForecasting, 2002, 21: 473-500.
[331] Sorenson H., Alspach D. Recursive Bayesian Estimation Using Gaussian Sums[J]. Auto-matica, 1971, 7: 465-479.
[332] Stanton R. A Nonparametric Model of Term Structure Dynamics and the Market Priceof Interest Rate Risk[J]. Journal of Finance, 1997, 52: 1973-2002.
[333] Stapleton R., Subrahmanyam M. The valuation of multivariate contingent claims indiscrete-time model[J]. Journal of Finance, 1984, 39: 207-228.
[334] Steeley J M. A two-factor model of the U.K. yield curve[J]. The Manchester SchoolSupplement, 1997, 65: 32-58.
[335] Sun L. Nonlinear drift and stochastic volatility: An empirical investigation of short-terminterest rate models[J]. The Journal of Financial Research, 2003, 26(3): 389-404
[336] Sun L. Regime shifts in interest rate volatility[J]. Journal of Empirical Finance, 2005,12: 418-434.
[337] Tanaka M., Katayama T. Robust Kalman filter for linear discrete-time system withGaussian sum noises[J]. International Journal of Systems Science, 1987, 18: 1721-1731.
[338] Tanizaki H., Mariano R. Prediction, Filtering and Smoothing in Nonlinear and Non-normal Cases Using Monte Carlo Integration[J]. Journal of Applied Econometrics, 1994, 9:163-179.
[339] Tanizaki H., Mariano R. Nonlinear and Nonnormal State-space Modeling with MonteCarlo Stochastic Simulation[J]. Journal of Econometrics, 1998, 83: 263-290.
[340] Tauchen G., Pitts M. The price variability-volume relationship on speculative markets[J].Econometrica, 1983, 51: 485-505.
[341] Taylor S J. Modelling stochastic volatility[J]. Mathematical Finance, 1994, 4: 183-204.
[342] Taylor S J., Xu X. The incremental volatility information in one million foreign exchangequotations[J]. Journal of Empirical Finance, 1997, 4: 317-340.
[343] Tera¨svirta T., Anderson H M. Characterizing nonlinearities in business cycles usingsmooth transition autoregressive models[J]. Journal of Applied Econometrics, 1992, 7: 119-136.
[344] Tierney L. Markov Chains for exploring Posterior Distributions (with discussion)[J]. TheAnnals of Statistics, 1994, 22: 1701-1786.
[345] Tse Y K. Some international evidence on the stochastic behavior of interest rates[J].Journal of lnternational Money and Finance, 1995, 14(5): 721-738.
[346] Tugnait J K. Detection and estimation for abruptly changing systems[J]. Automatica,1982, 18: 607-615.
[347] Turnbull S., Milne F. A simple approach to interest-rate option pricing[J]. Review ofFinancial Studies, 1991, 4: 81-121.
[348] Vasicek O. An equilibrium characterization of the term structure[J]. Journal of FinancialEconomics, 1977, 5: 177-188.
[349] Vetzal K. Stochastic volatility, movements in short term interest rates, and bond optionvalues[J]. Journal of Banking and Finance, 1997, 21: 169-196.
[350] Watanabe T. A non-linear filtering approach to stochastic volatility models with anapplication to daily stock returns[J]. Journal of Applied Econometrics, 1999, 14: 101-121.
[351] Weiss A A. ARMA models with ARCH errors[J]. Journal of Time Series Analysis, 1984,5(2): 129-143.
[352] Wiener N. Di?erential space[J]. Journal of Mathematics and Physics, 1923, 2: 131-174.
[353] Wiggins J B. Option values under stochastic volatility: theory and empirical estimates[J].Journal of Financial Economics, 1987, 19: 351-72.
[354] Yu J. On leverage in a stochastic volatility model[J]. Journal of Econometrics, 2005, 127:165-178.
[355] Yu J., Meyer R. Multivariate Stochastic Volatility Models: Bayesian Estimation. andModel Comparison[J]. Econometric Reviews, 2006, 25: 361-384.
[356] Yu J., Yang Z., Zhang X. A class of nonlinear stochastic volatility models and its impli-cations for pricing currency options[J]. Computational Statistics and Data Analysis, 2006,51(4): 2218-2231.
[357] Zucchini W., Guttorp P. A hidden Markov model for space-time precipitation[J]. WaterResources Research, 1991, 27: 1917-1923.
[1] Andersen T G., Bollerslev T., Diebold F X., Labys P. (Understanding, Optimizing, Usingand Forecasting) Realized Volatility and Correlation. Manuscript, Northwestern University,Duke University and University of Pennsylvania, 1999.
[2] Baba Y., Engle R F., Kraft D F., Kroner K F. Multivariate simultaneous general-ized ARCH, Department of Economics, University of California, San Diego, unpublishedmanuscript, 1991.
[3] Ball C A., Torous W N. A stochastic volatility model for the short-term interest ratesand the detection of structural shifts. Working Paper, Vanderbilt University, 1994.
[4] Bates D S. Pricing options on jump-di?usion processes. working paper, Rodney L. WhiteCenter, Wharton School, 1988.
[5] Casarin R. Bayesian Inference for Generalised Markov Switching Stochastic VolatilityModels. CEREMADE Journal Working Paper No. 0414, 2004.
[6] Chu B., Hwang S. The asymptotic properties of AR(1) process with the occasionallychanging AR coe?cient. Mimeo, Faculty of Finance, Cass Business School, London, 2006.
[7] Cox J. Notes on option pricing I: constant elasticity of variance di?usions. WorkingPaper, Stanford University, 1975.
[8] Du?ee G R. On the relation between the level and volatility of short-term interest rates:A comment on CKLS. Working Paper, Federal Reserve Board, Washington, 1993.
[9] Ghysels E., Jasiak J. Stochastic volatility and time deformation: an application to tradingvolume and leverage e?ects. manuscript, Universit′e de Montr′eal, 1996.
[10] Harvey A C. Long memory in stochastic volatility. Discussion Paper, London School ofEconomics, 1993.
[11] Hogan M., Weintraub K. The log-normal interest rate model and Eurodollar futures.Working paper, Citibank, New York, 1993.
[12] Jacquier E., Polson N G., Rossi P E. Models and prior distributions for multivariatestochastic volatility. Working Paper no. 95-18, CIRANO, 1994.
[13] Kim S., Shephard N. Stochastic volatility: Optimal likelihood inference and comparisonwith ARCH Model. Discussion Paper, Nu?eld College, Oxford, 1994.
[14] McManus D., Watt W. Estimating One-Factor Models of Short-Term Interest Rates.Bank of Canada Working Paper, 1999.
[15] Meddahi N. and Renault E. Aggregations and marginalisations of GARCH and stochasticvolatility models, discussion paper, GREMAQ, 1995.
[16] Oomen R C A. Modelling Realized Variance when Returns are Serially Correlated. Un-published manuscript. Warwick Business School, University of Warwick, 2002.
[17] Pitt M. Smooth particle filters for likelihood evaluation and maximisation. University ofWarwick working paper, 2002.
[18] Sandmann K., Sondermann D. A term structure model and the pricing of interest rateoptions. Working paper, University of Bonn, 1989.
[19] Schlo¨gl E., Schlo¨gl L. A tractable term structure model with endogenous interpolation andpositive interest rates. Working paper, University of Bonn, 1997.
[20] Shephard N G., Andersen T G. Stochastic volatility: origins and overview. EconomicsSeries Working Papers, University of Oxford, Department of Economics, 2008.
[21] Watanabe T., Asai M. Stochastic volatility models with heavy-tailed distributions: aBayesian analysis. Unpublished manuscript, Tokyo Metropolitan University, 2003.
[2]张世英、樊智:《协整理论与波动模型――金融时间序列分析及应用》,清华大学出版社,2004年。
[3] Abramowitz M., Stegun N. Handbook of Mathematical Functions[M]. Dover Publications,NY, 1970.
[4] Anderson B D O., Moore J B. Optimal Filtering[M]. Prentice Hall, Englewood Cli?s NJ,1979.
[5] Bhar R., Hamori S. Hidden Markov Models: Applications to Financial Economics[M].Dordrecht: Kluwer Academic, 2004.
[6] Bingham N H., Kiesel R. Risk-Neutral Valuation: Pricing and Hedging of FinancialDerivatives[M]. Springer Finance, London, 1998.
[7] Bjo¨rk T. Arbitrage Theory in Continuous Time[M]. Oxford University Press, 1998.
[8] Cappa′O., Moulines E., Ryd′en T. Inference in Hidden Markov Models[M]. Springer Seriesin Statistics. New York: Springer, 2005.
[9] Du?e D. Security Markets: Stochastic Models[M]. Academic Press, Boston, 1988.
[10] Durbin J., Koopman S J. Time Series Analysis by State Space Methods[M]. OxfordUniversity Press: Oxford, 2001.
[11] Engle R., Lee G. A long-run and short-run component model of stock return volatility.in Cointegration, Causality and Forecasting[M], edited by Engle R. and White H., OxfordUniversity Press, 1999.
[12] Fru¨hwirth-Schnatter S. Finite Mixture and Markov Switching Models[M]. Springer NewYork, 2006.
[13] Fuller W A. Introduction to Time Series (2nd edn)[M]. John Wiley, New York, 1996.
[14] Granger C W J., Tera¨asvirta T. Modelling Nonlinear Economic Relationships[M]. Oxford:Oxford University Press, 1993.
[15] Harvey A. Forecasting Structural Time Series Models and the Kalman Filter[M]. Cam-bridge University Press, Cambridge et al, 1990.
[16] Jackson J. A User’s Guide to Principal Components[M]. John Wiley, 1991.
[17] Kim C J., Nelson C R. State Space Models with Regime Switching, Classical and GibbsSampling Approaches with Applications[M]. Cambridge, MA: MIT Press, 1999.
[18] Krolzig H M. Markov-Switching Vector Autoregressions: Modelling, Statistical In-ference, and Application to Business Cycle Analysis[M]. New York/Berlin/Heidelberg:Springer,1997.
[19] Lemke W. Term Structure Modelling and Estimation in a State Space Framework[M].Springer, Berlin et al, 2006.
[20] Ripley B D. Stochastic Simulation[M]. John Wiley: New York, 1987.
[21] Taylor S J. Modeling Financial Time Series[M]. John Wiley: New York, 1986.
[22] Titterington D M., Smith A F M., Makov U E. Statistical analysis of finite mixturedistributions[M]. Chichester: John Wiley, 1985.
[23] Tsay R S. Analysis of Financial Time Series (2nd Edition)[M]. John Wiley and Sons,Inc, 2005.
[24] Wong C K J. Latent factor models of high frequency financial time series. UnpublishedPhD Thesis. University of Oxford, 2002.
[1] Anderson H M., Nam K., Vahid F. Asymmetric nonlinear smooth transition GARCHmodels. In Rothman P. (Ed.), Nonlinear Time Series Analysis of Economic and FinancialData, Boston: Kluwer, 1999: 191-207.
[2] Bansal R., Gallant A R., Hussey R., Tauchen G E. Computational aspects of nonparamet-ric simulation estimation. In Belsey D A. (Ed.), Computational Techniques for Econometricsand Economic Analysis. Boston, MA: Kluwer Academic Publishers, 1993: 3-22.
[3] Bates D S. Testing option pricing models. In Maddala G S., Rao C R. (Ed.), Handbookof Statistics, v. 14: Statistical Methods in Finance, Elsevier, Amsterdam, 1996a: 567-611.
[4] Black F. Studies in stock price volatility changes. Proceedings of the 1976 Business Meet-ing of the Business and Economic Statistics Section, American Statistical Association, 1976:177-181.
[5] Diebold F X., Lee J H., Weinbach G C. Regime switching with time-varying transitionprobabilities. In Hargreaves C P. (Ed.), Nonstationary Time Series Analysis and Cointegra-tion, 1994: 283-302. Oxford: Oxford University Press.
[6] Engle R F., Lee G. Estimating di?usions models of stochastic volatility. In Rossi P E.(Ed.), Modelling Stock Market Volatility: Bridging the Gap to Continuous Time, 1996: 333-355. San Diego: Academic Press.
[7] Gamerman D., Smith A F M. Bayesian analysis of longitudinal data studies. In BernardoJ M., Berger J O., Dawid A P., Smith A F M. (Ed.), Bayesian Statistics, 5, 1996: 587-597.Oxford: Oxford University Press.
[8] Hamilton J. State-space models. In Engle R., McFadden D. (Ed.), Handbook of Econo-metrics Volume 4, 1994: 3039-3080. Amsterdam: North-Holland.
[9] Harvey A C. Long-memory in stochastic volatility. In Knight J., Satchell S. (Ed.), Fore-casting Volatility in Financial Markets. Oxford: Butterworth-Heineman, 1998: 307-320.
[10] Jacquier E., Polson N G., Rossi P E. Stochastic volatility: univariate and multivariate ex-tensions. Computing in Economics and Finance 112, Society for Computational Economics,1999.
[11] Palm F. Garch models of volatility. In ByMaddala G., Rao C. (Ed.), Handbook of Statis-tics, 1996: 209-240, Elsevier Science, Amsterdam.
[12] Pen?a D., Guttman I. Bayesian approach to robustifying the Kalman filter. In Spall J C.(Ed.), Bayesian Analysis of Time Series and Dynamic Linear Models, 1988: 227-253. NewYork: Marcel Dekker.
[13] Schnatter S., Gutknecht D., Kirnbauer R. A Bayesian approach to estimating the pa-rameters of a hydrological forecasting system. In Viertl R. (Ed.), Probability and BayesianStatistics, 1987: 415-422. New York: Plenum.
[14] Shephard N G. Statistical aspects of ARCH and stochastic volatility. in Cox D R.,Bamdor?-Nielson 0 E., Hinkley D V. (Ed.), Time Series Models in Econometrics, Financeand Other Fields (London: Chapman & Hall),1996: 1-67.
[15] Taylor S J. Financial returns modeled by the product of two stochastic processes, a studyof daily sugar prices 1961-79. In Time Series Analysis: Theory and Practice 1, AndersonOD (Ed.). North-Holland: Amsterdam, 1982: 203-226.
[1]白崑、张世英:扩展SV模型及其在深圳股票市场的应用[J],《系统工程》2001年第19卷第6期。
[2]曹阳、李剑武:人民币实际汇率水准波动对进出口贸易的影响-基于1980-2004年的实证研究[J],《世界经济研究》2006年第150期。
[3]陈敏、王国明、吴国富、蒋学雷:中国证券市场的ACD-GARCH模型及其应用[J],《统计研究》2003年第11期。
[4]董乐:我国短期利率均值回复假设的实证研究[J],《数量经济技术经济研究》2006年第11期。
[5]杜子平、张世英:SV模型的聚合及其边际化研究[J],《系统工程理论方法应用》2002年第11卷第2期。
[6]范龙振:上交所债券利率期限结构与两因子Vasicek模型[J],《复旦学报(自然科学版)》2003年第5期。
[7]韩伟、李钢:高频金融数据的长记忆SV模型分析――基于FFF回归[J],《西北农林科技大学学报(社会科学版)》2006年第6卷第2期。
[8]洪永淼、林海:中国市场利率动态研究――基于短期国债回购利率的实证分析[J],《经济学(季刊)》2006年第5期。
[9]蒋祥林、王春峰、吴晓霖:基于状态转移ARCH模型的中国股市波动性研究[J],《系统工程》2004年第3期。
[10]柯珂、张世英:ARCH模型的诊断分析[J],《管理科学学报》2001年第4期。
[11]李成、马国校:VaR模型在我国银行同业拆借市场中的应用研究[J],《金融研究》2007年第5期。
[12]李付军:SV-GED模型在中国股市的VaR与ES度量及分析[J],《系统工程理论方法应用》2006年第15卷第1期。
[13]李汉东、张世英:随机波动模型的持续性和协同持续性研究[J],《系统工程学报》2002年第17卷第4期。
[14]李汉东、张世英:ARCH模型与SV模型之间的关系研究[J],《系统工程学报》2003年第18卷第2期。
[15]刘丹红、张世英、黄涛、蒋孝胜:LMSV模型波动的长记忆与相关性的小波分析[J],《统计与决策》2007年第6期。
[16]刘凤芹、吴喜之:基于SV模型的深圳股市波动的预测[J],《山西财经大学学报》2004年第26卷第4期。
[17]刘继春:多维GARCH模型的估计和检验[J],《吉林大学学报(自然科学版)》2000年第4期。
[18]刘金全、崔畅:中国沪深股票市场收益率与波动性的实证研究[J],《经济学(季刊)》2002年第3期。
[19]刘金全、郑挺国:我国货币政策冲击对实际产出周期波动的非对称影响分析[J],《数量经济技术经济研究》2006年第10期。
[20]刘金全、郑挺国、隋建利:我国通货膨胀率均值过程和波动过程中的双长记忆性度量与统计检验[J],《管理世界》2007年第7期。
[21]卢志红、郑丕谔:GARCH族模型在上海股市分阶段对比分析中的应用[J],《中国计量学院学报》2004年第1期.
[22]孟利锋、张世英、何信a:具有杠杆效应SV模型的贝叶斯分析及其应用[J],《系统工程》2004年第22卷第3期。
[23]孟利锋、张世英、何信b:SV模型参数估计的经验特征函数方法[J],《系统工程》2004年第22卷第12期。
[24]苏卫东、齐安甜、黄兴:长记忆SV模型的统计性质及其实证分析[J],《系统工程》2004年第22卷第3期。
[25]苏卫东、张世英:随机波动模型估计及在金融风险防范中的应用[J],《天津大学学报》2002年第35卷第3期。
[26]苏卫东、张世英:变截距SV模型及其在上海股市的实证[J],《系统工程理论方法应用》2003年第12卷第1期。
[27]苏卫东、张世英:多元长记忆SV模型及其在沪深股市的应用[J],《管理科学学报》2004年第7卷第1期。
[28]王炳雪、史忠科、阎东明:基于趋势平滑和GARCH的证券市场预测[J],《西安理工大学学报》2002年第18期。
[29]王春峰、蒋祥林、吴晓霖:随机波动性模型的比较分析[J],《系统工程学报》2005年第20卷第2期。
[30]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年第9期。
[31]王宇新:GARCH模型和SV模型对深圳股市的比较[J],《合肥工业大学学报(自然科学版)》2007年第30卷第6期。
[32]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年第22期。
[33]吴长凤:利用回归GARCH模型对我国沪深股市的分析[J],《预测》1999年第4期。
[34]谢赤、吴雄伟:基于Vasicek模型和CIR模型中的中国货币市场利率行为实证分析[J],《中国管理科学》2002年第3期。
[35]徐梅、张世英a:基于小波变换的时变长记忆SV模型估计方法研究[J],《系统工程学报》2006年第21卷第1期。
[36]徐梅、张世英b:基于小波变换的长记忆随机波动模型估计方法研究[J],《中国管理科学》2006年第14卷第1期。
[37]许启发、张世英:Box-Cox-SV模型及其对金融时间序列刻画能力研究[J],《系统工程学报》2005年第20卷第4期。
[38]战雪丽、张世英:基于Copula-SV模型的金融投资组合风险分析[J],《系统管理学报》2007年第16卷第3期。
[39]张瑞锋、张世英:基于VS-MSV模型的金融市场波动溢出分析及实证研究[J],《系统工程》2007年第25卷第8期。
[40]张若东、孙王杰、刘继春:多维门限GARCH模型的平稳遍历性[J],《东北师大学报:自然科学版》2003年第1期。
[41]张世英、柯珂:ARCH模型体系[J],《系统工程学报》2002年第17卷第3期。
[42]赵华:人民币汇率与利率之间的价格和波动溢出效应研究[J],《金融研究》2007年第3期。
[43]赵振全、苏治、丁志国:我国股票市场收益率非对称均值回归特征的计量检验――基于ANST-GARCH模型的实证分析[J],《数量经济技术经济研究》2005年第4期。
[44]周宏山、冀云:非对称随机波动模型在中国股市的应用[J],《统计与信息论坛》2007年第22卷第4期。
[45]周彦、张世英:基于MCMC方法的连续时间SV模型建模研究[J],《工业工程》2007年第10卷第1期。
[46]周彦、张世英、张彤:跳跃连续时间SV模型建模及实证研究[J],《系统管理学报》2007年第16卷第5期。
[47] Aase K K. Contingent claims valuation when the security price is a combination of an Ito?process and a random point process[J]. Stochastic Processes and Their Applications, 1988,28: 185-220.
[48] Abraham B., Balakrishna N., Sivakumar R. Gamma stochastic volatility models[J]. Jour-nal of Forecasting, 2006, 25: 153-171.
[49] Ackerson G A., Fu K S. On state estimation in switching environments[J]. IEEE Trans-actions on Automatic Control, 1970, 15: 10-17.
[50] Aguilar O., West M. Bayesian dynamic factor models and variance matrix discountingfor portfolio allocation[J]. Journal of Business and Economic Statistics, 2000, 18: 338-357.
[51] Ahn D., Gao B. A parametric nonlinear model of term structure dynamics[J]. Review ofFinancial Studies, 1999, 12: 721-762.
[52] A¨?t-Sahalia Y. Nonparametric pricing of interest rate derivatives[J]. Econometrica, 1996a,64: 527-560.
[53] A¨?t-Sahalia Y. Testing continuous-time models of the spot interest rate[J]. Review ofFinancial Studies, 1996b, 9: 385-426.
[54] Akashi H., Kumamoto H. Random sampling approach to state estimation in switchingenvironments[J]. Automatica, 1977, 13: 429-434.
[55] Albert J H., Chib S. Bayes inference via Gibbs sampling of autoregressive time seriessubject to Markov mean and variance shifts[J]. Journal of Business and Economic Statistics,1993, 11: 1-15.
[56] Alexander S S.Price movements in speculative markets: trends or random walks[J]. In-dustrial Management Review, 1961, 2: 7-26.
[57] Alspach D L., Sorenson H W. Nonlinear Bayesian estimation using Gaussian sum ap-proximations[J]. IEEE Transactions on Automatic Control, 1972, 17: 439-448.
[58] Amin K., Jarrow R. Pricing options on risky assets in a stochastic interest rate econ-omy[J]. Mathematical Finance, 1992, 2: 217-237.
[59] Amin K., Ng V. Option valuation with systematic stochastic volatility[J]. Journal ofFinance, 1993, 48: 881-910.
[60] Anderson T G. Stochastic autogregssive volatility: a framework for volatility modeling[J].Mathematical Finance, 1994b, 4: 75-102.
[61] Andersen T G., Bollerslev T. Answering the skeptics: Yes, standard volatility models doprovide accurate forecasts[J]. International Economic Review, 1998, 39: 885-905.
[62] Andersen T G., Bollerslev T., Diebold F X., Labys P. The distribution of exchange ratevolatility[J]. Journal of the American Statistical Association, 2001, 96: 42-55.
[63] Andersen T G., Bollerslev T., Diebold F X., Labys P. Modeling and forecasting realizedvolatility[J]. Econometrica, 2003, 71: 579-625.
[64] Andersen T G., Bollerslev T., Meddahi N. Analytic evaluation of volatility forecasts[J].International Economic Review, 2004, 45: 1079-1110.
[65] Andersen T G., Lund J. Estimating continuous-time stochastic volatility models of theshort-term interest rate[J]. Journal of Econometrics, 1997, 77: 343-377.
[66] Andersen, T G., S?rensen B E. GMM Estimation of a stochastic volatility model: aMonte Carlo study[J]. Journal of Business and Economic Statistics, 1997, 14: 328-352.
[67] Andreou E., Ghysels E. Detecting multiple breaks in financial market volatility dynam-ics[J]. Journal of Applied Econometrics, 2002, 17: 579-600.
[68] Ang A., Bekaert G. Regime switches in interest rates[J]. Journal of Business and Eco-nomic Statistics, 2002, 20: 163-182.
[69] Areal N M P C., Taylor S J. The realized volatility of FTSE-100 futures prices[J]. Journalof Futures Markets, 2002, 22: 627-648.
[70] Asai M. Autoregressive stochastic volatility models with heavy-tailed distributions: Acomparison with multifactor volatility models[J]. Journal of Empirical Finance, 2008, 15:332-341.
[71] Asai M., McAleer M. Dynamic asymmetric leverage in stochastic volatility models[J].Econometric Reviews, 2005, 24: 317-332.
[72] Asai M., McAleer M. Asymmetric multivariate stochastic volatility[J]. Econometric Re-views, 2006, 25: 453-473.
[73] Bachelier L. Theories de la speculation. Ann. Sci. Ecole Norm. Sup, 1900, 17: 21-28.
[74] Bailey W., Stulz E. The pricing of stock index options in a general equilibrium model[J].Journal of Financial and Quantitative Analysis, 1989, 24: 1-12.
[75] Baillie R T., Bollerslev T. The message in daily exchange rates: a conditional-variancetale[J]. Journal of Business and Economic Statistics, 1989, 7: 297-305.
[76] Baillie R T., Bollerslev T., Mikkelson H O. Fractionally integrated generalized autore-gressive conditional heteroskedasticity[J]. Journal of Econometrics, 1996, 74: 3-30.
[77] Bakshi G., Cao C., Chen Z. Empirical performance of alternative options pricing mod-els[J]. Journal of Finance, 1997, 52(5): 2003-2049.
[78] Balduzzi P., Das S., Foresi S., Sundaram, R. A simple approach to threefactor a?ne termstructure models[J]. Journal of Fixed Income, 1996, 6: 43-53.
[79] Balke N., Fomby T B. Shifting trends, segmented trends, and infrequent permanentshocks[J]. Journal of Monetary Economics, 1991, 28: 61-85.
[80] Ball C A., Torous W N. On jumps in common stock prices and their impact on calloption pricing[J]. Journal of Finance, 1985, 40: 155-173.
[81] Ball C A., Torous W N. The stochastic volatility of short-term interest rates: someinternational evidence[J]. Journal of Finance, 1999, 54: 2339-2359.
[82] Bar-Shalom Y., Tse E. Tracking in a cluttered environment with probabilistic data as-sociation[J]. Automatica, 1975, 11: 451-460.
[83] Bardhan I., Chao X. Pricing options on securities with discontinuous returns[J]. Stochas-tic Processes and Their Application, 1993, 48: 123-137.
[84] Barndor?-Nielsen O E., Shephard N. Econometric analysis of realised volatility and itsuse in estimating stochastic volatility models[J]. Journal of the Royal Statistical Society B,2002, 64: 253-280.
[85] Bates D S. The crash of 87: Was it expected? the evidence from option markets[J].Journal of Finance, 1991, 46: 1009-1044.
[86] Bates D S. Jumps and stochastic volatility: exchange rate processes implicit in PHLXDeutschmark options[J]. Review of Financial Studies, 1996b, 9(1): 69-107.
[87] Baum L E., Petrie T. Statistical inference for probabilistic functions of finite state Markovchains[J]. The Annals of Mathematical Statistics, 1966, 37: 1554-1563.
[88] Bauwens L., Laurent S., Rombouts J V K. Multivariate GARCH models: A survey[J].Journal of Applied Econometrics, 2006, 21: 79-109.
[89] Beckers S. A note on estimating the parameters of the di?usion-jump model of stockreturns[J]. Journal of Financial and Quantitative Analysis, 1981, 16(1): 127-140.
[90] Berg A., Meyer R., Yu J. Deviance information criterion for comparing stochastic volatil-ity models[J]. Journal of Business and Economic Statistics, 2004, 22: 107-120.
[91] Bickel P J., Ritov Y., Ryd′en T. Asymptotic normality of the maximum likelhood esti-mator for general hidden Markov models[J]. The Annals of Statistics, 1998, 26: 1614-1635.
[92] Black F., Scholes M. The pricing of options and corporate liabilities[J]. Journal of PoliticalEconomy, 1973, 81: 637-654.
[93] Black F., Derman E., Toy W. A one-factor model of interest rates and its application toTreasury bond options[J]. Financial Analysis Journal, 1990, 46(1): 33-39.
[94] Black F., Karasinski P. Bond and option pricing when short rates are lognormal[J].Financial Analysts Journal, 1991, 47(4):52-59.
[95] Blair B J., Poon S H., Taylor S J. Forecasting S&P 100 volatility: The incrementalinformation content of implied volatilities and high frequency index returns[J]. Journal ofEconometrics, 2001, 105: 5-16.
[96] Bliss R R., Smith D C. The elasticity of interest rate volatility: Chan, Karolyi, Longsta?,and Sanders revisited[J]. Journal of Risk, 1998, 1(1): 21-46.
[97] Blom H., Bar-Shalom Y. The interacting multiple model algorithm for systems withMarkovian switching coe?cients[J]. IEEE Transactions on Automatic Control, 1988, 33:780-783.
[98] Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Eco-nomics, 1986, 31: 307-327.
[99] Bollerslev T. Modelling the coherence in short-run nominal exchange rates: A multivari-ate generalized ARCH approach[J]. Review of Economics and Statistics, 1990, 72: 498-505.
[100] Bollerslev T. A Conditionally Heteroskedastic Time Series Model for Speculative Pricesand Rates of Return[J]. Review of Economics and Statistics, 1987, 69: 542-47.
[101] Bollerslev T., Chou R Y., Kroner K F. ARCH modeling in finance[J]. Journal of Econo-metrics, 1992, 52: 5-59.
[102] Bollerslev T., Engle R F., Wooldridge J. A capital asset pricing model with time varyingcovariances[J]. Journal of Political Economy, 1988, 96: 116-131.
[103] Brailsford T J., Maheswaran K. The dynamics of the Australian short-term interestrate[J]. Australian Journal of Management, 1998, 23: 213-234.
[104] Breidt F J., Crato N., de Lima P J F. The detection and estimation of longmemory instochastic volatility[J]. Journal of Econometrics, 1998, 83: 325-348.
[105] Brennan M J. The pricing of contingent claims in discrete time models[J]. Journal ofFinance, 1979, 34: 53-68.
[106] Brennan M J., Schwartz E S. Savings bonds, retractable bonds and callable bonds[J].Journal of Financial Economics, 1977, 5: 67-88.
[107] Brennan M J., Schwartz E. A continuous-time approach to the pricing of bonds[J].Journal of Banking and Finance, 1979, 3: 133-155.
[108] Brennan M J., Schwartz E S. Analyzing convertible bonds[J]. Journal of Financial andQuantitative Analysis, 1980, 15(4): 907-929.
[109] Brennan M J., Schwartz E S. An Equilibrium Model of Bond Pricing and a Test ofMarket E?ciency[J]. Journal of Financial and Quantitative Analysis, 1982, 17(3): 301-329.
[110] Brenner R J., Harjes R H., Kroner K F. Another look at models of the short-term interestrate[J]. Journal of Financial and Quantitative Analysis, 1996, 31(1): 85-107.
[111] Brown S J., Dybvig P H. Empirical implications of the Cox, Ingersoll, Ross theory ofthe term structure of interest rates[J]. Journal of Finance, 1986, 41: 143-172.
[112] Byers S L., Nowman K B. Forecasting UK and US interest rates using continuous timeterm structure models[J]. International Review of Financial Analysis, 1998, 7: 191-206.
[113] Cai J. A Markov model of switching-regime ARCH[J]. Journal of Business and EconomicStatistics, 1994,12: 309-316.
[114] Carter C K., Kohn R. On Gibbs sampling for state space models[J]. Biometrika, 1994,81: 541-553.
[115] Carter C., Kohn R. Semiparametric Bayesian inference for time series with mixed spec-tra[J]. Journal of the Royal Statistical Society B, 1997, 255-268.
[116] Carvalho C M. and Lopes H F. Simulation-based sequential analysis of Markov switchingstochastic volatility models[J]. Computational Statistics and Data Analysis, 2007, 51: 4526-4542.
[117] Cavaliere G. Asymptotics for unit root tests under Markov regime-switching[J]. Econo-metrics Journal, 2003, 6: 193-216.
[118] Chan K., Karolyi G., Longsta? F., Sanders A. An empirical comparison of alternativemodels of the short-term interest rate[J]. Journal of Finance, 1992a, 47(3): 1209-1227.
[119] Chan K., Karolyi G., Longsta? F., Sanders A. The volatility of Japanese interest rates: Acomparison of alternative term structure models[J]. Pacific-Basin Capital Markets Research,1992b, 3: 119-136.
[120] Chapman D A., Pearson N D. Recent advances in estimating term structure models[J].Financial Analysts Journal, 2001, 57(3): 77-95.
[121] Chen L. Stochastic mean and stochastic volatility three-factor model of the term struc-ture of interest rates and its applications in derivatives pricing and risk management[J].Financial Markets, Institutions and Instruments, 1996, 5(1): 1-18.
[122] Chen R R., Scott L. Pricing interest rate options in a two-factor Cox-Ingersoll-Rossmodel of the term structure[J]. Review of Financial Studies, 1992, 5: 613-636.
[123] Chernov M., Gallant A R., Ghysels E., Tauchen G. Alternative models for stock pricedynamics[J]. Journal of Econometrics, 2003, 116: 225-257.
[124] Chesney M., Scott L O. Pricing European currency options: a comparison of the modifiedBlack-Scholes model and a random variance model[J]. Journal of Financial QuantitativeAnalysis, 1989, 24: 267-284.
[125] Chib S. Bayes estimation of regressions with autoregressive errors: a Gibbs samplingapproach[J]. Journal of Econometrics, 1993, 58: 275-294.
[126] Chib S. Calculating posterior distributions and modal estimates in Markov mixturemodels[J]. Journal of Econometrics, 1996, 75: 79-97.
[127] Chib S., Nardari F., Shephard N. Markov chain Monte Carlo methods for generalizedstochastic volatility models[J]. Journal of Econometrics, 2002, 108: 281-316.
[128] Chib S., Nardari F., Shephard N. Analysis of high-dimensional multivariate stochasticvolatility models[J]. Journal of Econometrics, 2006, 134: 341-371.
[129] Chow G C. Tests of equality between sets of coe?cients in two linear linear regressions(Ref: 74V42 p601-608)[J]. Econometrica, 1960, 28: 591-605.
[130] Chow H K. Robust estimation in time series: an approximation to the Gaussian sumfilter[J]. Communications in Statistics - Theory and Methods, 1994, 23: 3491-3505.
[131] Clark P K. A subordinated stochastic process model with fixed variance for speculativeprices[J]. Econometrica , 1973,41: 135-156.
[132] Conley T G., Hansen L P., Luttmer E G J., Scheinkman J A. Short-term interest ratesas subordinated di?usions[J]. Review of Financial Studies, 1997, 10(3): 525-577.
[133] Constantinides G. A theory of the nominal term structure of interest rates[J]. Review ofFinancial Studies, 1992, 5: 531-552.
[134] Cosslett S R., Lee L F. Serial correlation in latent discrete variable models[J]. Journalof Econometrics, 1985, 27: 79-97.
[135] Cox J C., Ross S A. The valuation of options for alternative stochastic processes[J].Journal of Financial Economics, 1976, 3: 145-166.
[136] Cox J C., Ingersoll J., Ross S A. An analysis of variable rate loan contracts[J]. Journalof Finance, 1980, 35: 389-403.
[137] Cox J C., Ingersoll J., Ross S A. A theory of the term structure of interest rates[J].Econometrica, 1985, 53(2): 385-407.
[138] Dahlquist M. On alternative interest rate processes[J]. Journal of Banking and Finance,1996, 20: 1093-1119.
[139] Dalang R., Morton A. and Willinger W. Equivalent martingale measures and no arbitragein stochastic security market models[J], Stochastics and Stochastic Reports,1989, 29: 185-202.
[140] Dai Q., Singleton K J. Specification analysis of a?ne term structure models[J]. Journalof Finance, 2001, 55: 1943-1978.
[141] Danielsson J. Stochastic volatility in asset prices: Estimation with simulated maximumlikelihood[J]. Journal of Econometrics, 1994, 61: 375-400.
[142] Danielsson J. Multivariate stochastic volatility models: estimation and a comparisonwith VGARCH models[J]. Journal of Empirical Finance, 1998, 5: 155-173.
[143] Danielsson J., Richard J F. Accelerated Gaussian importance sampler with applicationto dynamic latent variable models[J]. Journal of Applied Econometrics, 1993, 8: 153-173.
[144] Das S R. The surprise element: Jumps in interest rates[J]. Journal of Econometrics,2002, 106: 27-65.
[145] de Jong P., Shephard N. The simulation smoother for time series models[J]. Biometrika,1995, 82: 339-350.
[146] Derman E., Kani I. Riding on a smile[J]. Risk, 1994, 7: 32-39.
[147] Derman E., Ergener D., Kani I. Static options replication[J]. Journal of Derivatives,1995, 2: 78-95.
[148] Dickey D A., Fuller W A. Likelihood ratio statistics for autoregressive time series witha unit root[J]. Econometrica , 1981, 49: 1057-1072.
[149] Diebold F X. Modeling the persistence of conditional variances: A comment[J]. Econo-metric Reviews, 1986, 5: 51-56.
[150] Diebold F X., Nerlove M. The dynamics of exchange rate volatility: a multivariate latentfactor GARCH model[J]. Journal of Applied Econometrics, 1989, 4: 1-21.
[151] Ding Z., Granger C W J., Engle R F. A long memory property of stock market returnsand a new model[J]. Journal of Empirical Finance, 1993, 1: 83-108.
[152] Dothan U. On the term structure of interest rates[J]. Journal of Financial Economics,1978, 7: 229-264.
[153] Du?e D., Kan R. A yield-factor model of interest rates[J]. Mathematical Finance, 1996,6: 379-406.
[154] Du?e D., Singleton K J. Simulated moments estimation of Markov models of assetprices[J]. Econometrica, 1993, 61: 929-952.
[155] Dupire B. Pricing with a smile[J]. Rsik, 1994, 7: 18-20.
[156] Durbin J., Koopman S J. Time series analysis of non-Gaussian observations based onstate space models from both classical and Bayesian perspectives (with discussion)[J]. Jour-nal of the Royal Statistical Society B, 2000, 62: 3-56.
[157] Durham G B. Likelihood-based specification analysis of continuous-time models of theshort-term interest rates[J]. Journal of Financial Economics, 2003, 70(3): 463-487.
[158] Durham G B. Monte Carlo methods for estimating, smoothing, and filtering one- andtwo-factor stochastic volatility models[J]. Journal of Econometrics, 2005, 133: 273-305.
[159] Dueker M. Markov switching in GARCH processes and meanreverting stock-marketvolatility[J]. Journal of Business and Economic Statistics, 1997, 15: 26-34.
[160] Durbin J., Koopman S J. Monte Carlo maximum likelihood estimation for non-Gaussianstate space models[J]. Biometrika, 1997, 84: 669-684.
[161] Engel C., Hamilton J D. Long swings in the Dollar: Are they in the data and do marketsknow it? [J].The American Economic Review, 1990, 80: 689-713.
[162] Engle R F. Autoregressive conditional heteroscedasticity with estimates of the varianceof United Kingdom in?ation[J]. Econometrica, 1982, 50: 987-1007.
[163] Engle R F., Kroner K F. Multivariate simultaneous generalized ARCH[J]. EconometricTheory, 1995, 11: 122-50.
[164] Engle R F., Lilien D M., Robins R P. Estimating time varying term premis in the termstructure: the ARCH-M model[J]. Econometrica, 1987, 55(2): 391-407.
[165] Engle R F., Ng V K. Measuring and testing the impact of news on volatility[J]. Journalof Finance , 1993, 48: 1749-1801.
[166] Eraker B. MCMC analysis of di?usion models with application to finance[J]. Journal ofBusiness and Economic Statistics, 2001, 19: 177-191.
[167] Fama E F. The stable paretian distribution[J]. Journal of Business, 1963, 36: 420-429.
[168] Fama E F. The behavior of stock market prices[J]. Journal of Business, 1965, 38: 34-105.
[169] Filardo A J. Business-cycle phases and their transitional dynamics[J]. Journal of Busi-ness and Economic Statistics, 1994, 12: 299-308.
[170] Filardo A J., Gordon S F. Business cycle duration[J]. Journal of Econometrics, 1998,85: 99-123.
[171] Fiorentini G., Leo′n A., Rubio G. Estimation and empirical performance of Heston’sstochastic volatility model: The case of a thinly traded market[J]. Journal of EmpiricalFinance, 2002, 9: 225-255.
[172] Fleming J., Kirby C., Ostdiek B. Information and volatility linkages in the stock, bondand money markets[J]. Journal of Financial Economics, 1998, 49:111-137.
[173] Fong H G., Vasicek O A. Fixed Income Volatility Management[J]. The Journal of Port-folio Management, 1991, 17(4): 41-46.
[174] Fornari F., Mele A. Modeling the changing asymmetry of conditional variances[J]. Eco-nomics Letters, 1996, 50: 197-203.
[175] Fornari F., Mele A. Sign- and volatility-switching ARCH models: theory and applicationsto international stock markets[J]. Journal of Applied Econometrics, 1997, 12: 49-65.
[176] Francq C., Roussignol M., Zakoian J. Conditional heteroscedasticity driven by hiddenMarkov chains[J]. Journal of Time Series Analysis, 2001, 22: 197-220.
[177] French K R., Schwert G W., Stambaugh R F. Expected Stock Returns and Volatility[J].Journal of Financial Economics, 1987, 19: 3-29.
[178] Fridman M., Harris L. A Maximum Likelihood Approach for Non-Gaussian StochasticVolatility Models[J]. Journal of Business and Economic Statistics, 1998, 16: 284-291.
[179] Fru¨hwirth-Schnatter S., Kaufmann S. Model-based clustering of multiple time series[J].Journal of Business and Economic Statistics, 2008, 26(1): 78-89.
[180] Gallant A R., Tauchen G E. Which moments to match?[J]. Econometric Theory, 1996,12: 657-681.
[181] Gallant A R., Tauchen G E. Reprojecting partially observed systems with application tointerest rate di?usions[J]. Journal of the American Statistical Association, 1998, 93: 10-24.
[182] Gelfand A E., Smith A F M., Lee T M. Bayesian Analysis of constrained parametersand truncated data problems using Gibbs Sampling[J]. Journal of the American StatisticalAssociation, 1992, 87: 523-532.
[183] Geman S., Geman D. Stochastic relaxation, Gibbs distributions and the Bayesian restora-tion of images[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984,6: 721-741.
[184] Geweke J F. Bayesian inference in econometric models using Monte Carlo integration[J].Econometrica, 1989, 57: 1317-1339.
[185] Geweke J F. Using simulation methods for Bayesian econometric models: inference,development and communication[J]. Econometric Reviews, 1999, 18: 1-127.
[186] Gibbons M R., Rarnaswamy K. A test of the Cox, Ingersoll and Ross model of the termstructure[J]. Review of Financial Studies, 1993, 6: 619-658.
[187] Glosten L R., Jagannathan R., Runkle D E. On the relation between the expected valueand the volatility of the nominal excess return on stocks[J]. Journal of Finance, 1993, 48:1779-1801.
[188] Goldfeld S., Quandt R. A Markov model for switching regression[J]. Journal of Econo-metrics, 1973, 1: 3-16.
[189] Gordon K., Smith A F M. Modeling and monitoring biomedical time series[J]. Journalof the American Statistical Association, 1990, 85: 328-337.
[190] Gordon N., Salmond D., Smith A. A Novel Approach to Non-linear and Non-GaussianBayesian State Estimation[J]. IEE Proceedings, 1993, 140: 107-133.
[191] Gouri′eroux C.,Monfort A., Renault E. Indirect inference[J]. Journal of Applied Econo-metrics, 1993, 8: 85-118.
[192] Granger C W J., Hyung N. Occasional structural breaks and long memory with anapplication to the S&P500 absolute stock returns[J]. Journal of Empirical Finance, 2004,11: 399-421.
[193] Granger C W J., Morris M. Time series modeling and interpretation[J]. Journal of theRoyal Statistical Society A, 1976, 139: 246-257.
[194] Gray S F. Modeling the conditional distribution of interest rates as a regime-switchingprocess[J]. Journal of Financial Economics, 1996, 42: 27-62.
[195] Hall S G., Psaradakis Z., Sola M. Cointegration and changes in regime: The Japaneseconsumption function. Journal of Applied Econometrics, 1997, 12: 151-168.
[196] Hall S G., Psaradakis Z., Sola M. Detecting periodically collapsing bubbles: A Markov-switching unit root test[J]. Journal of Applied Econometrics, 1999, 14: 143-154.
[197] Hamilton J D. Rational expectations econometric analysis of changes in regime: Aninvestigation on the term structure of interest rates[J]. Journal of Economic Dynamics andControl, 1988, 12: 385-423.
[198] Hamilton J D. A New Approach to the Economic Analysis of Nonstationary Time Seriesand the Business Cycle[J]. Econometrica, 1989, 57(2): 357-384.
[199] Hamilton J D., Lin G. Stock market volatility and the business cycle[J]. Journal ofApplied Econometrics, 1996, 11: 573-593.
[200] Hamilton J D., Susmel R. Autoregressive conditional heteroscedasticity and changes inregime[J]. Journal of Econometrics, 1994, 64: 307-333.
[201] Hamilton J D. Specification testing in Markov-switching time-series models[J]. Journalof Econometrics, 1996, 70: 127-157.
[202] Hansen L P. Large sample properties of generalized method of moments estimators[J].Econometrica, 1982, 50: 1029-1054.
[203] Harrison M., Kreps D. Martingale and arbitrage in multiperiod securities markets[J].Journal of Economic Theory, 1979, 20: 381-408.
[204] Harrison P J., Stevens C F. Bayesian Forecasting[J]. Journal of the Royal StatisticalSociety Series B, 1976, 38: 205-247.
[205] Harvey A., Ruiz E., Shephard N. Multivariate stochastic variance models[J]. Review ofEconomic Studies, 1994, 61: 247-264.
[206] Harvey A C., Shephard N. The estimation of an asymmetric stochastic volatility modelfor asset returns[J]. Journal of Business and Economic Statistics, 1996, 14: 429-434.
[207] Heston S I. A closed form solution for options with stochastic volatility with applicationsto bond and currency options[J]. Review of Financial Studies, 1993, 6: 327-344.
[208] Hiraki T., Takezawa N. How sensitive is short-term Japanese interest rate volatility tothe level of the interest rate?[J]. Economics Letters, 1997, 56: 325-332.
[209] Hogan M. Problems in certain two-factor term structure models[J]. Annals of AppliedProbability, 1993, 3: 576-581.
[210] Holst U., Lindgren G., Holst J., Thuvesholmen M. Recursive estimation in switchingautoregressions with a Markov regime[J]. Journal of Time Series Analysis, 1994, 15: 489-506.
[211] Hong Y., Li H., Zhao F. Out-of-sample performance of discrete-time spot interest ratemodels[J]. Journal of Business and Economic Statistics, 2004, 22: 457-473.
[212] Hsieh D A. Modeling heteroskedasticity in daily foreign exchange rates. Journal of Busi-ness and Economic Statistics, 1989, 7: 307-317.
[213] Hsieh D A. Chaos and nonlinear dynamics: application to financial markets[J]. Journalof Finance, 1991, 46: 1839-1877.
[214] Hull J., White A. The pricing of options on assets with stochastic volatilities[J]. Journalof Finance, 1987, 42: 281-300.
[215] Hull J C., White A. Pricing interest-rate derivative securities[J]. The Review of FinancialStudies, 1990, 3(4): 573-592.
[216] Hull J C., White A. One-factor interest-rate models and the valuation of interest-ratederivative securities[J]. Journal of Financial and Quantitative Analysis, 1993, 28: 235-254.
[217] Hull J., White A. Numerical procedures for implementing term structure models I: single-factor Models[J]. Journal of Derivatives, 1994, 2, 7-16.
[218] Hwang S., Valls P. Small sample properties of GARCH estimates and persistence[J].European Journal of Finance, 2006, 12: 473-494.
[219] Hwang S., Satchell S E., Valls P. How persistent is stock return volatility? An answerwith Markov regime switching stochastic volatility models[J]. Journal of Business Financeand Accounting, 2007, 34: 1002-1024.
[220] Jacquier E., Polson N G., Rossi P E. Bayesian analysis of stochastic volatility models(with discussion)[J]. Journal of Business and Economic Statistics, 1994, 12: 371-417.
[221] Jacquier E., Polson N G., Rossi P E. Bayesian analysis of stochastic volatility modelswith fat-tails and correlated errors[J]. Journal of Econometrics, 2004, 122: 185-212.
[222] Jamshidian F. A simple class of square-root interest-rate models. Applied MathematicalFinance, 1995, 2: 61-72.
[223] Jeanblanc-Picqu′e M., Pontier M. Optimal portfolio for a small investor in a market withdiscontinuous prices[J]. Applied Mathematical Optimisation, 1990, 22: 287-310.
[224] Jiang G. Stochastic volatility and jump-di?usion-implications on option pricing[J]. In-ternational Journal of Theoretical and Applied Finance, 1999, 2: 409-440.
[225] Johnson H., Shanno D. Option pricing when the variance is changing[J]. Journal ofFinancial and Quantitative Analysis, 1987, 22: 143-152.
[226] Kalimipalli M., Susmel R. Regime-Switching stochastic volatility and short-term interestrates[J]. Journal of Empirical Finance, 2004, 11: 309-329.
[227] Karlsen H A., Tj?theim D. Autoregressive segmentation of signal traces with applica-tion to geological dipmeter measurements[J]. IEEE Transactions on Geoscience and RemoteSensing, 1990, 28: 171-181.
[228] Kaufmann S., Fru¨hwirth-Schnatter S. Bayesian analysis of switching ARCH models[J].Journal of Time Series Analysis, 2002, 23: 425-458.
[229] Kawakatsu H. Numerical integration-based Gaussian mixture filters for maximum likeli-hood estimation of asymmetric stochastic volatility models[J]. Econometrics Journal, 2007,10: 342-358.
[230] Kim C J. Sources of monetary growth uncertainty and economic activity: The time-varying parameter model with heteroscedastic disturbances[J]. The Review of Economicsand Statistics, 1993a, 75: 483-492.
[231] Kim C J. Unobserved-component time series models with Markovswitching heteroscedas-ticity: Changes in regime and the link between in?ation rates and in?ation uncertainty[J].Journal of Business and Economic Statistics, 1993b, 11: 341-349.
[232] Kim C J. Dynamic Linear Models with Markov-Switching[J]. Journal of Econometrics,1994, 60: 1-22.
[233] Kim D., Kon S J. Structural change and time dependence in models of stock returns[J].Journal of Empirical Finance, 1999, 6: 283-308.
[234] Kim I M. A dynamic programming approach to the estimation of Markov switchingregression models[J]. Journal of Statistical Computation and Simulation, 1993c, 45: 61-76.
[235] Kim S., Shephard N., Chib S. Stochastic Volatility: Likelihood Inference and Comparisonwith ARCH Models[J]. Review of Economic Studies, 1998, 65: 361-393.
[236] Kitagawa G. Non-Gaussian State Space Modeling of Nonstationary Time Series (withdiscussion)[J]. Journal of the American Statistical Association, 1987, 82: 1032-1063.
[237] Kitagawa G. Monte Carlo Filter and Smoother for Non-Gaussian Non-linear State SpaceNodels[J]. Journal of Computational and Graphical Statistics, 1996, 5: 1-25.
[238] Klaasen F. Improving GARCH volatility forecasts with regime-switching GARCH[J].Empirical Economics, 2002, 27: 363-394.
[239] Knight J L., Yu J. The empirical characteristic function in time series estimation[J].Econometric Theory, 2002, 18: 691-721.
[240] Knight J L., Satchell S E., Yu J. Estimation of the stochastic volatility model by the em-pirical characteristic function method[J]. Australian and New Zealand Journal of Statistics,2002, 44: 319-335.
[241] Koedijk K G., Nissen F G J A., Scotchman P C., Wol? C C P. The dynamics of short-term interest rate volatility reconsidered[J]. European Finance Review, 1997, 1: 105-130.
[242] Koopman S J., Uspensky E H. The stochastic volatility in mean model - empiricalevidence from international stock markets[J]. Journal of Applied Econometrics, 2002, 17:667-689.
[243] Krolzig H M. Business cycle measurement in the presence of structural change: Interna-tional evidence[J]. International Journal of Forecasting, 2001, 17: 349-368.
[244] Krolzig H M., Sensier M. A disaggregated Markov-switching model of the business cyclein UK manufacturing[J]. The Manchester School, 2000, 68: 442-460.
[245] Lam P S. The Hamilton model with a general autoregressive component: Estimation andcomparison with other models of economic time series[J]. Journal of Monetary Economics,1990, 26: 409-432.
[246] Lamoureux C G., Lastrapes W D. Persistence in variance, structural change, and theGARCH model[J]. Journal of Business and Economic Statistics, 1990, 8: 225-234.
[247] Lastrapes W D. Exchange rate volatility and U.S. monetary policy: an ARCH applica-tion[J]. Journal of Money, Credit and Banking, 1989, 21: 66-77.
[248] Leroux B G. Maximum-likelihood estimation for hidden Markov models[J]. StochasticProcesses and Their Applications, 1992, 40: 127-143.
[249] Leybourne S J., Mills T C., Newbold P. Spurious rejections by Dickey-Fuller tests in thepresence of a break under the null[J]. Journal of Econometrics, 1998, 87: 191-203.
[250] Liesenfeld R., Jung R C. Stochastic volatility models: conditional normality versusheavy-tailed distributions[J]. Journal of Applied Econometrics, 2000, 15: 137- 160.
[251] Liesenfeld R., Richard J F. Univariate and multivariate stochastic volatility models:estimation and diagnostics[J]. Journal of Empirical Finance, 2003, 10: 505-531.
[252] Lin D K., Guttman I. Handling spuriosity in the Kalman filter[J]. Statistics and Proba-bility Letters, 1993, 16: 259-268.
[253] Lindgren G. Markov regime models for mixed distributions and switching regressions[J].Scandinavian Journal of Statistics, 1978, 5: 81-91.
[254] Lintner J. The valuation of risky assets, the selection of risky investment in stock port-folios, capital budgets[J]. Review of Economics, Statistics, 1965, 47: 13-37.
[255] Litterman R, Scheinkman J. Common factors a?ecting bond returns[J]. Journal of FixedIncome, 1991, 1: 54-61.
[256] Litterman R., Scheinkman J., Weiss L. Volatility and the Yield Curve[J]. The Journalof Fixed Income,1991, 1: 49-53.
[257] Lo A. Maximum likelihood estimation of generalized Ito? processes with discretely sam-pled data[J]. Econometric Theory, 1988, 4: 231-247.
[258] Longsta? F A. A nonlinear general equilibrium model of the term structure of interestrates[J]. Journal of Financial Economics, 1989, 23: 195-224.
[259] Longsta? F A., Schwartz E S. Interest rate volatility and the term structure: A two-factor general equilibrium model[J]. Journal of Finance, 1992, 47: 1259-1282.
[260] Lumsdaine R L., Papell D H. Multiple trend breaks and the unit root hypothesis[J]. TheReview of Economics and Statistics, 1997, 79: 212-218.
[261] Mahieu R., Schotman P. An empirical application of stochastic volatility models[J].Journal of Applied Econometrics, 1998, 13: 333-360.
[262] Mandelbrot B B. The variation of certain speculative prices[J]. Journal of Business,1963, 36: 394-416.
[263] Markowitz M H. Portfolio selection[J]. Journal of F inance , 1952, 7(1): 77-91.
[264] McCulloch R E., Tsay R S. Bayesian inference of trend- and di?erence-stationarity[J].Econometric Theory, 1994a, 10: 596-608.
[265] McCulloch R E., Tsay R S. Statistical analysis of economic time series via Markovswitching models[J]. Journal of Time Series Analysis, 1994, 15: 523-539.
[266] Melino A., Turnbull S M. Pricing foreign currency options with stochastic volatility[J].Journal of Econometrics, 1990, 45: 239-265.
[267] Merton R C. The theory of rational option pricing[J]. Bell Journal of Economics, 1973,4(1): 141- 183.
[268] Merton R C. Option pricing when underlying stock returns are discontinuous[J]. Journalof Financial Economics, 1976, 3: 125-144.
[269] Merton R C. On estimating the expected return on the market: An exploratory investi-gation[J]. Journal of Financial Economics, 1980, 8: 323-361.
[270] Meyer R., Yu J. BUGS for a Bayesian analysis of stochastic volatility models[J]. Econo-metrics Journal, 2000, 3: 198-215.
[271] Mikosch T., Starica C. Nonstationarities in financial time series, the long-range depen-dence, and the IGARCH e?ects[J]. Review of Economics and Statistics, 2004, 86: 378-390.
[272] Mossin J. Equilibrium in a capital asset market[J]. Econometrica, 1966, 34: 768-783.
[273] Naik V. Option valuation and hedging strategies with jumps in the volatility of assetreturns[J]. Journal of Finance, 1993, 48: 1969-1984.
[274] Nakajima J., Omori Y. Leverage, heavy-tails and correlated jumps in stochastic volatilitymodels[J]. Computational Statistics and Data Analysis, 2008, doi:10.1016/j.csda.2008.03.015.
[275] Neftci S N. Are economic time series asymmetric over the business cycle?[J]. Journal ofPolitical Economy, 1984, 92: 307-328.
[276] Nelson D B. Stationarity and persistence in the GARCH(1,1) model[J]. EconometricTheory, 1990a, 6: 318-334.
[277] Nelson D B. ARCH models as di?usion approximations[J]. Journal of Econometrics,1990b, 45: 7-38.
[278] Nelson D B. Conditional heteroskedasticity in asset returns: a new approach[J]. Econo-metrica, 1991, 59: 347-370.
[279] Nelson C R., Piger J., Zivot E. Markov regime switching and unit-root tests[J]. Journalof Business and Economic Statistics, 2001, 19: 404-415.
[280] Nowman K B. Gaussian estimation of single-factor continuous time models of the termstructure of interest rates[J]. Journal of Finance, 1997, 52(4): 1695-1706.
[281] Nowman K B. Continuous-time short term interest rate models[J]. Applied FinancialEconomics, 1998, 8: 401-407.
[282] Nowman K B. The volatility of Japanese interest rates: Evidence for certificate of depositand gensaki rates[J]. International Review of Financial Analysis, 2002, 11: 29-38.
[283] Omori Y., Chib S., Shephard N., Nakajima J. Stochastic volatility with leverage: fastand e?cient likelihood inference[J]. Journal of Econometrics, 2007, 140: 425-449.
[284] Pagan A R., Schwert G W. Alternative models for conditional stock volatility[J]. Journalof Econometrics, 1990, 45: 267-290.
[285] Pearson N D., Sun T S. Exploiting the conditional density in estimating the term struc-ture: an application to the Cox, Ingersoll and Ross model[J]. Journal of Finance, 1994, 49:1279-1304.
[286] Pennacchi G G. Identifying the dynamics of real interest rates and inf lation: Evidenceusing survey data[J]. Review of Financial Studies, 1991, 4: 53-86.
[287] Perron P. The great crash, the oil price shock, and the unit root hypothesis[J]. Econo-metrica, 1989, 57: 1361-401.
[288] Petrie T. Probabilistic functions of finite state Markov chains[J]. The Annals of Mathe-matical Statistics, 1969, 40: 97-115.
[289] Phillips K L. A two-country model of stochastic output with changes in regime[J]. Journalof International Economics, 1991, 31: 121-142.
[290] Pitt M., Shephard N. Filtering via Simulation: Auxiliary Particle Filter[J]. Journal ofthe American Statistical Association, 1999, 94: 590-599.
[291] Poon S H., Taylor S. Macroeconomic factors and the UK stock market[J]. Journal ofBusiness, Finance and Accounting, 1991, 18(5): 619-636.
[292] Poon S H., Granger C W J. Forecasting volatility in financial markets: a review[J].Journal of Economic Literature, 2003, 41: 478-539.
[293] Press J. A compound events model for security prices[J]. Journal of Business, 1967, 40:317-335.
[294] Psaradakis Z. Markov-level shifts and the unit-root hypothesis[J]. The EconometricsJournal, 2001, 4: 225-241.
[295] Psaradakis Z. On the asymptotic behaviour of unit root tests in the presence of a Markovtrend[J]. Statistics & Probability Letters, 2002, 57: 101-109.
[296] Quandt R E. A new approach to estimating switching regressions[J]. Journal of theAmerican Statistical Association, 1972, 67: 306-310.
[297] Rabiner L R. A tutorial on hidden Markov models and selected applications in speechrecognition[J]. Proceedings of the IEEE, 1989, 77, 257-286.
[298] Ray B K., Tsay R S. Long-range dependence in daily stock volatilities[J]. Journal ofBusiness and Economic Statistics, 2000, 18: 254-262.
[299] Richard S F. An arbitrage model of the term structure of interest rates[J]. Journal ofFinancial Economics, 1978, 6: 33-57.
[300] Rogers L C G. Gaussian errors[J]. Risk, 1996, 9(1): 42-45.
[301] Ross S A. The arbitrage theory of capital asset pricing[J]. Journal of Economic Theory,1976, 13: 341-360.
[302] Rubinstein M. The valuation of uncertain income streams and the pricing of options[J].Bell Journal of Economics, 1976, 7: 407-425.
[303] Rubinstein M. Implied binomial trees[J]. Journal of Finance, 1994, 69: 771-818.
[304] Ruiz E. Quasi-maximum likelihood estimation of stochastic volatility models[J]. Journalof Econometrics, 1994, 63: 289-306.
[305] Samuelson P. Rational theory of warrant pricing[J]. Industrial Management Review, 1965,6: 13-32.
[306] Sandmann K. The pricing of options with an uncertain interest rate: a discrete-timeapproach[J]. Mathematical Finance, 1993, 3: 201-216.
[307] Sandmann K., Sondermann D. A term structure model and the pricing of interest ratederivatives[J]. Review of Futures Markets, 1993, 12(2): 391-423.
[308] Sandmann K., Sondermann D. On the stability of log-normal interest rate models andthe pricing of Eurodollar futures[J]. Mathematical Finance, 1997, 7(2): 119-125.
[309] Sandmann G., Koopman S J. Estimation of stochastic volatility models via Monte Carlomaximum likelihood[J]. Journal of Econometrics, 1998, 87: 271-301.
[310] Sclove S L. Time series segmentation: A model and a method[J]. Information Science,1983, 29: 7-25.
[311] Scott L. Option pricing when the variance changes randomly: theory, estimators, andapplications[J]. Journal of Financial and Quantitative Analysis, 1987, 22: 419-438.
[312] Scott L. Pricing stock options in a jump-di?usion model with stochastic volatility andinterest rates: Applications of fourier inversion methods[J]. Mathematical Finance, 1997, 7:413-426.
[313] Sharpe W. Capital asset prices:a theory of market equilibrium under conditions of risk[J].Journal of Finance, 1964, 19: 425-442.
[314] Shephard N G. Fitting non-linear time series models, with application to stochasticvariance models[J]. Journal of Applied Econometrics, 1993, 8: 135-152.
[315] Shepard N. Partial non-Gaussian state space[J]. Biometrika, 1994, 81: 115-131.
[316] Shephard N G. Discussion of Durbin and Koopman[J]. Journal of the Royal StatisticalSociety, Series B, 2000, 62, 30-32.
[317] Shephard N G., Kim S. Comment on E. Jacquier, N. Polson and E. Rossi [J]. Journal ofBusiness and Economic Statistics, 1994, 12: 406-410.
[318] Shephard N G., Pitt M K. Likelihood analysis of non-Gaussian measurement time se-ries[J]. Biometrika, 1997, 84: 653-667.
[319] Shumway R H., Sto?er D S. Dynamic linear models with switching[J]. Journal of theAmerican Statistical Association, 1991, 86: 763-769.
[320] Singleton K J. Estimation of a?ne asset pricing models using the empirical characteristicfunction[J]. Journal of Econometrics, 2001, 102: 111-141.
[321] van der Sluis P J. Emmpack 1.01: C/C++ code for use with Ox for estimation ofunivariate stochastic volatility models with the e?cient method of moments[J]. Studies inNonlinear Dynamics and Econometrics, 1997, 2(3): 77-94.
[322] Smith D R. Markov-Switching and stochastic volatility di?usion models of short-terminterest rates[J]. Journal of Business and Economic Statistics, 2002, 20: 183-197.
[323] Smith A F M., Gelfand A E. Bayesian statistics without tears: a samplingresamplingperspective[J]. American Statistican, 1992, 46:84-88.
[324] Smith A F M., Roberts G O. Bayesian computation via the Gibbs sampler and relatedMarkov chain Monte Carlo methods[J]. Journal of the Royal Statistical society, 1993, 55:3-23.
[325] Smith A F M., West M. Monitoring renal transplants: An application of the multiprocessKalman filter[J]. Biometrics, 1983, 39: 867-878.
[326] So M K P., Choi C Y. A multivariate threshold stochastic volatility model[J]. Mathe-matics and Computers in Simulation, 2008, doi:10.1016/j.matcom.2007.12.003.
[327] So M K P., Lam K., Li W K. Multivariate modelling of the autoregressive randomvariance process[J]. Journal of Time Series Analysis, 1997, 18(4): 429-446.
[328] So M K P., Lam K., Li W K. A stochastic volatility model with Markov switching[J].Journal of Business and Economic Statistics, 1998, 16: 244-253.
[329] So M K P., Li W K. Bayesian unit root testing in stochastic volatility models[J]. Journalof Business and Economic Statistics, 1999, 17: 491-496.
[330] So M K P., Li W K., Lam K. A threshold stochastic volatility model[J]. Journal ofForecasting, 2002, 21: 473-500.
[331] Sorenson H., Alspach D. Recursive Bayesian Estimation Using Gaussian Sums[J]. Auto-matica, 1971, 7: 465-479.
[332] Stanton R. A Nonparametric Model of Term Structure Dynamics and the Market Priceof Interest Rate Risk[J]. Journal of Finance, 1997, 52: 1973-2002.
[333] Stapleton R., Subrahmanyam M. The valuation of multivariate contingent claims indiscrete-time model[J]. Journal of Finance, 1984, 39: 207-228.
[334] Steeley J M. A two-factor model of the U.K. yield curve[J]. The Manchester SchoolSupplement, 1997, 65: 32-58.
[335] Sun L. Nonlinear drift and stochastic volatility: An empirical investigation of short-terminterest rate models[J]. The Journal of Financial Research, 2003, 26(3): 389-404
[336] Sun L. Regime shifts in interest rate volatility[J]. Journal of Empirical Finance, 2005,12: 418-434.
[337] Tanaka M., Katayama T. Robust Kalman filter for linear discrete-time system withGaussian sum noises[J]. International Journal of Systems Science, 1987, 18: 1721-1731.
[338] Tanizaki H., Mariano R. Prediction, Filtering and Smoothing in Nonlinear and Non-normal Cases Using Monte Carlo Integration[J]. Journal of Applied Econometrics, 1994, 9:163-179.
[339] Tanizaki H., Mariano R. Nonlinear and Nonnormal State-space Modeling with MonteCarlo Stochastic Simulation[J]. Journal of Econometrics, 1998, 83: 263-290.
[340] Tauchen G., Pitts M. The price variability-volume relationship on speculative markets[J].Econometrica, 1983, 51: 485-505.
[341] Taylor S J. Modelling stochastic volatility[J]. Mathematical Finance, 1994, 4: 183-204.
[342] Taylor S J., Xu X. The incremental volatility information in one million foreign exchangequotations[J]. Journal of Empirical Finance, 1997, 4: 317-340.
[343] Tera¨svirta T., Anderson H M. Characterizing nonlinearities in business cycles usingsmooth transition autoregressive models[J]. Journal of Applied Econometrics, 1992, 7: 119-136.
[344] Tierney L. Markov Chains for exploring Posterior Distributions (with discussion)[J]. TheAnnals of Statistics, 1994, 22: 1701-1786.
[345] Tse Y K. Some international evidence on the stochastic behavior of interest rates[J].Journal of lnternational Money and Finance, 1995, 14(5): 721-738.
[346] Tugnait J K. Detection and estimation for abruptly changing systems[J]. Automatica,1982, 18: 607-615.
[347] Turnbull S., Milne F. A simple approach to interest-rate option pricing[J]. Review ofFinancial Studies, 1991, 4: 81-121.
[348] Vasicek O. An equilibrium characterization of the term structure[J]. Journal of FinancialEconomics, 1977, 5: 177-188.
[349] Vetzal K. Stochastic volatility, movements in short term interest rates, and bond optionvalues[J]. Journal of Banking and Finance, 1997, 21: 169-196.
[350] Watanabe T. A non-linear filtering approach to stochastic volatility models with anapplication to daily stock returns[J]. Journal of Applied Econometrics, 1999, 14: 101-121.
[351] Weiss A A. ARMA models with ARCH errors[J]. Journal of Time Series Analysis, 1984,5(2): 129-143.
[352] Wiener N. Di?erential space[J]. Journal of Mathematics and Physics, 1923, 2: 131-174.
[353] Wiggins J B. Option values under stochastic volatility: theory and empirical estimates[J].Journal of Financial Economics, 1987, 19: 351-72.
[354] Yu J. On leverage in a stochastic volatility model[J]. Journal of Econometrics, 2005, 127:165-178.
[355] Yu J., Meyer R. Multivariate Stochastic Volatility Models: Bayesian Estimation. andModel Comparison[J]. Econometric Reviews, 2006, 25: 361-384.
[356] Yu J., Yang Z., Zhang X. A class of nonlinear stochastic volatility models and its impli-cations for pricing currency options[J]. Computational Statistics and Data Analysis, 2006,51(4): 2218-2231.
[357] Zucchini W., Guttorp P. A hidden Markov model for space-time precipitation[J]. WaterResources Research, 1991, 27: 1917-1923.
[1] Andersen T G., Bollerslev T., Diebold F X., Labys P. (Understanding, Optimizing, Usingand Forecasting) Realized Volatility and Correlation. Manuscript, Northwestern University,Duke University and University of Pennsylvania, 1999.
[2] Baba Y., Engle R F., Kraft D F., Kroner K F. Multivariate simultaneous general-ized ARCH, Department of Economics, University of California, San Diego, unpublishedmanuscript, 1991.
[3] Ball C A., Torous W N. A stochastic volatility model for the short-term interest ratesand the detection of structural shifts. Working Paper, Vanderbilt University, 1994.
[4] Bates D S. Pricing options on jump-di?usion processes. working paper, Rodney L. WhiteCenter, Wharton School, 1988.
[5] Casarin R. Bayesian Inference for Generalised Markov Switching Stochastic VolatilityModels. CEREMADE Journal Working Paper No. 0414, 2004.
[6] Chu B., Hwang S. The asymptotic properties of AR(1) process with the occasionallychanging AR coe?cient. Mimeo, Faculty of Finance, Cass Business School, London, 2006.
[7] Cox J. Notes on option pricing I: constant elasticity of variance di?usions. WorkingPaper, Stanford University, 1975.
[8] Du?ee G R. On the relation between the level and volatility of short-term interest rates:A comment on CKLS. Working Paper, Federal Reserve Board, Washington, 1993.
[9] Ghysels E., Jasiak J. Stochastic volatility and time deformation: an application to tradingvolume and leverage e?ects. manuscript, Universit′e de Montr′eal, 1996.
[10] Harvey A C. Long memory in stochastic volatility. Discussion Paper, London School ofEconomics, 1993.
[11] Hogan M., Weintraub K. The log-normal interest rate model and Eurodollar futures.Working paper, Citibank, New York, 1993.
[12] Jacquier E., Polson N G., Rossi P E. Models and prior distributions for multivariatestochastic volatility. Working Paper no. 95-18, CIRANO, 1994.
[13] Kim S., Shephard N. Stochastic volatility: Optimal likelihood inference and comparisonwith ARCH Model. Discussion Paper, Nu?eld College, Oxford, 1994.
[14] McManus D., Watt W. Estimating One-Factor Models of Short-Term Interest Rates.Bank of Canada Working Paper, 1999.
[15] Meddahi N. and Renault E. Aggregations and marginalisations of GARCH and stochasticvolatility models, discussion paper, GREMAQ, 1995.
[16] Oomen R C A. Modelling Realized Variance when Returns are Serially Correlated. Un-published manuscript. Warwick Business School, University of Warwick, 2002.
[17] Pitt M. Smooth particle filters for likelihood evaluation and maximisation. University ofWarwick working paper, 2002.
[18] Sandmann K., Sondermann D. A term structure model and the pricing of interest rateoptions. Working paper, University of Bonn, 1989.
[19] Schlo¨gl E., Schlo¨gl L. A tractable term structure model with endogenous interpolation andpositive interest rates. Working paper, University of Bonn, 1997.
[20] Shephard N G., Andersen T G. Stochastic volatility: origins and overview. EconomicsSeries Working Papers, University of Oxford, Department of Economics, 2008.
[21] Watanabe T., Asai M. Stochastic volatility models with heavy-tailed distributions: aBayesian analysis. Unpublished manuscript, Tokyo Metropolitan University, 2003.