基于GARCH和COPULA的天津房地产市场预测
摘要
房地产行业是人们生活的基本保障，和人民生活质量密切相关，也是中国国民经济的主导产业，在现代社会经济生活中有着举足轻重的地位。2000年以后，全国大多数城市房价一直呈上涨趋势。今后房价是否会继续上涨，到底能上涨到什么价位，无论对于政府、开发商，还是普通市民都是非常关心的问题。房价和成交面积是房地产市场两个重要指标，从它们不断变化的数据中找到不变规律，建立时间序列模型，预测天津市房价和成交面积未来概率分布。
预测一般要求数据平稳，采用单位根检验验证天津市2005年3月20日到2007年10月31日每日平均房价、市区房价和成交面积对数变化率平稳性。存在许多预测模型，到底哪一种更适合本文数据，利用独立性检验、代替数据线性检验和条件异方差效应检验，确定自回归滑动-条件异方差(ARMA-GARCH)模型。不同阶数的模型会影响预测效果，通过检验标准残差独立性和信息准则选取合适阶数。最后极大似然估计模型参数。
预测未来房价和成交面积的概率分布必须知道残差的概率分布。因为房价和成交面积的大起大落更受人们关注，所以利用广义帕累特分布(GPD)得到房价和成交面积变化率标准残差尾部分布，非尾部分布采用正态分布。因为要考虑房价和成交面积的联合分布，所以还需知道它们之间相关结构(COPULA)。COPULA类型很多，必须选择合适数据的某种类型。依据极大似然函数值，从40种COPULA中选择最优COPULA，极大似然估计参数。为了衡量房价和成交面积变化率中一个出现大值，另外一个也出现大值的可能性，计算3种尾部相关系数。
通常预测都是给出一个数值，但是每天房价和成交面积肯定存在随机波动，所以运用蒙特卡罗方法预测后200天天津市房价、成交面积和市区房价概率分布。基于拟合Copula产生伪随机标准残差，按照拟合边缘分布(尾部GPD模型，非尾正态分布)分位数函数逆转。按照ARMA-GARCH拟合模拟预测变化率均值和标准波动，计算均值+标准波动×标准残差伪随随机数，逆变换变化率为原始数据。重复模拟1000次，把每天1000个样本的经验分布当成底分布，计算均值、中位数、80%VaR和95% VaR。根据2007年11月1日到2007年12月26日实际数据验证了预测结果的有效性。
Real estate, deciding the level of living quantity, is the base of people’s livingand the key industry of national economy. It plays an important role in modern socialactivity. Housing price in most cities has been rising since 2000. It is interesting forgovernment, enterprize and people whether the price will go on rising and what extentit reach. Housing price and take-up areas are the two crucial indicators of real estatemarket. Invariant rule is found from changing data. Time series model is established topredict probability distribution of the two indicator of Tianjin in the future.
Prediction generally requires stationary series. Daily average housing price ofurban and city in Tianjin and take-up areas from March 20, 2005 to October 31, 2007were test for stationary by unit-root test through logarithm return. ARMA-GARCHmodel was guaranteed among lots of models by independence test, surrogate data testand conditional heteroscedasticity test. The order of the model will in?uence forecaste?ect. Suitable order was made out by information criteria and testing independence ofresiduals. Parameters were estimated by maximum likelihood.
Forecasting price and area’s distribution dependents on residuals’distribution.Their extreme behavior is paid more people’s attention, so tail distribution was obtainedby generalized Pareto distribution(GPD). The rest was modeled by normal distribution.In order to know joint probability distribution, Copula is needed. Appropriate Copulawas selected from 40 kinds of Copula by maximum likelihood function. Three tail de-pendence coe?cients, measuring the probability of one indicator appearing large valueconditioning another have large value, were computed.
Always a number is predicted. But daily price and area must exit stochastic viola-tion, so probability distributions in the future 200 days were predicted by Monte Carlo.Pseudo random numbers, generated from fitted Copula, were transformed according tofitted tail and non-tail quantile function. Mean and deviation of predicted return weregot by fitted ARMA-GARCH model. Raw price and area were calculated through re-versing mean plus deviation times Pseudo random numbers. The empirical distributionof 1000 repeated simulations was regarded as underlying distribution. Mean, median,80% VaR and 95% VaR were estimated. The data from November 1, 2007 to December26, 2007 testified the validity of the prediction results.
预测一般要求数据平稳，采用单位根检验验证天津市2005年3月20日到2007年10月31日每日平均房价、市区房价和成交面积对数变化率平稳性。存在许多预测模型，到底哪一种更适合本文数据，利用独立性检验、代替数据线性检验和条件异方差效应检验，确定自回归滑动-条件异方差(ARMA-GARCH)模型。不同阶数的模型会影响预测效果，通过检验标准残差独立性和信息准则选取合适阶数。最后极大似然估计模型参数。
预测未来房价和成交面积的概率分布必须知道残差的概率分布。因为房价和成交面积的大起大落更受人们关注，所以利用广义帕累特分布(GPD)得到房价和成交面积变化率标准残差尾部分布，非尾部分布采用正态分布。因为要考虑房价和成交面积的联合分布，所以还需知道它们之间相关结构(COPULA)。COPULA类型很多，必须选择合适数据的某种类型。依据极大似然函数值，从40种COPULA中选择最优COPULA，极大似然估计参数。为了衡量房价和成交面积变化率中一个出现大值，另外一个也出现大值的可能性，计算3种尾部相关系数。
通常预测都是给出一个数值，但是每天房价和成交面积肯定存在随机波动，所以运用蒙特卡罗方法预测后200天天津市房价、成交面积和市区房价概率分布。基于拟合Copula产生伪随机标准残差，按照拟合边缘分布(尾部GPD模型，非尾正态分布)分位数函数逆转。按照ARMA-GARCH拟合模拟预测变化率均值和标准波动，计算均值+标准波动×标准残差伪随随机数，逆变换变化率为原始数据。重复模拟1000次，把每天1000个样本的经验分布当成底分布，计算均值、中位数、80%VaR和95% VaR。根据2007年11月1日到2007年12月26日实际数据验证了预测结果的有效性。
Real estate, deciding the level of living quantity, is the base of people’s livingand the key industry of national economy. It plays an important role in modern socialactivity. Housing price in most cities has been rising since 2000. It is interesting forgovernment, enterprize and people whether the price will go on rising and what extentit reach. Housing price and take-up areas are the two crucial indicators of real estatemarket. Invariant rule is found from changing data. Time series model is established topredict probability distribution of the two indicator of Tianjin in the future.
Prediction generally requires stationary series. Daily average housing price ofurban and city in Tianjin and take-up areas from March 20, 2005 to October 31, 2007were test for stationary by unit-root test through logarithm return. ARMA-GARCHmodel was guaranteed among lots of models by independence test, surrogate data testand conditional heteroscedasticity test. The order of the model will in?uence forecaste?ect. Suitable order was made out by information criteria and testing independence ofresiduals. Parameters were estimated by maximum likelihood.
Forecasting price and area’s distribution dependents on residuals’distribution.Their extreme behavior is paid more people’s attention, so tail distribution was obtainedby generalized Pareto distribution(GPD). The rest was modeled by normal distribution.In order to know joint probability distribution, Copula is needed. Appropriate Copulawas selected from 40 kinds of Copula by maximum likelihood function. Three tail de-pendence coe?cients, measuring the probability of one indicator appearing large valueconditioning another have large value, were computed.
Always a number is predicted. But daily price and area must exit stochastic viola-tion, so probability distributions in the future 200 days were predicted by Monte Carlo.Pseudo random numbers, generated from fitted Copula, were transformed according tofitted tail and non-tail quantile function. Mean and deviation of predicted return weregot by fitted ARMA-GARCH model. Raw price and area were calculated through re-versing mean plus deviation times Pseudo random numbers. The empirical distributionof 1000 repeated simulations was regarded as underlying distribution. Mean, median,80% VaR and 95% VaR were estimated. The data from November 1, 2007 to December26, 2007 testified the validity of the prediction results.
引文
[1]闫 妍,许 伟,部 慧,等.基于TEI@I方法论的房价预测方法[J].系统工程理论与实践, 2007(7):1–9, 51.
[2] International Institute for Urban Development of Beijin . China City LivingQuality Report No.1[R].[S.l.]: 2006 China City Forum Beijing Summ, 2006.
[3] Malpezzi S. A simple error correction model of housing prices[J]. Journal ofHousing Economics, 1999, 8(1):27–62.
[4] Seko M. Housing prices and economic cycles[C]//The International ConferenceonHousingMarket and the Macro Economy. Hong Kong: [s.n.] , 2003.
[5] Anglin P. Local dynamics and contagion in real estate markets[C]//The InternationalConference on Real Estates and Macro Economy. Beijing: [s.n.] , 2006.
[6] Liu J G, Zhang X L, Wu W P. Application of fuzzy neural network for realestate prediction[J]. ADVANCES IN NEURAL NETWORKSISNN 2006, PT 3,PROCEEDINGS, 2006, 3973:1187–1191.
[7] Zhou W X, Sornette D. Analysis of the real estate market in Las Vegas:Bubble, seasonal patterns, and prediction of the CSW indices[J]. Physica A:Statistical Mechanics and its Applications, 2008, 387(1):243– 260. http://dx.doi.org/10.1016/j.physa.2007.08.059. Econophysics;Real estatemarket;Power law;.
[8] Wedyawati W, Lu M. Mining real estate listings using ORACLE data warehousingand predictive regression[C]//. United States: Las Vegas, NV, 2004:296–301. Predictive data mining;Regression;Real estate multiple listing service;Datamining technology;.
[9] Bin O. A prediction comparison of housing sales prices by parametricversus semi-parametric regressions[J]. Journal of Housing Economics,2004, 13(1):68–84. http://www.sciencedirect.com/science/article/B6WJR-4BSVPMJ-1/2/65ed4dc9c7eefc532ca702230156be0f.
[10] Case B, Clapp J, Dubin R, et al. Modeling Spatial and Temporal House Price Patterns:A Comparison of Four Models[J]. The Journal of Real Estate Finance andEconomics, 2004, 29(2):167–191. http://dx.doi.org/10.1023/B:REAL.0000035309.60607.53.
[11] Clapp J M, Giaccotto C. Evaluating House Price Forecasts[J].Journal of Real Estate Research, 2002, 24(1):1–26. available athttp://ideas.repec.org/a/jre/issued/v24n12002p1-26.html.
[12]王婧,田澎.小波神经网络在房地产价格指数预测中的应用[J].计算机仿真,2005(7):96–98.
[13]杨楠,邢力聪.灰色马尔可夫模型在房价指数预测中的应用[J].统计与信息论坛, 2006, 21(5):52–55.
[14]龙会典,张海燕.基于ARIMA模型的广州市商品房价格预测[J].商业研究,2007(7):211–213.
[15]李岳,黄河,王启星,等.国内平均房价增长的极限[J].统计与决策,2003(6):56–56.
[16] Pollatsek A, Tversky A N. A theory of risk[J]. Journal of Mathematical Psychology,1970, 7:540–553.
[17] Ramsay C M. Loading gross premiums for risk without using utility theory(withDiscussions)[J]. Transactions of the Society of Actuaries XLV, 1994, 48:305–349.
[18] Artzner P, Delbaen J M, F. adn Eber, Heath D. Coherent measure of risk[J].Mathematical Finance, 1999, 9:203–208.
[19]王爱民,何 信.金融风险统计度量标准研究[J].统计研究, 2005(2):67–71.
[20] Brock D W, W.A., Scheinkman J. A test for independence based on the correlationdimension[R].[S.l.]: University of Wisconsin-Madison and University ofChicago, 1986.
[21] Theiler J, Eubank S, Longtin A, et al. Testing for nonlinearity in time series: themethod of surrogate data[J]. Physica D Nonlinear Phenomena, 1992, 58:77–94.
[22] Dickey D, Fuller W. Distribution of the estimators for autoregressive time serieswith a unit root[J]. Journal of the American Statistical Association, 1979,74:427–431.
[23] Said S E, Dickey D A. Testing for Unit Roots in Autoregressive-Moving AverageModels of Unknown Order[J]. Biometrika, 1984, 71:599–607.
[24] Perron P. Trends and Random Walks in Macroeconomic Time Series[J]. Journalof Economic Dynamics and Control, 1988, 12:297–332.
[25] Kwiatkowski D, Phillips P C B, Schmidt P, et al. Testing the Null Hypothesis ofStationarity against the Alternative of a Unit Root[J]. Journal of Econometrics,1992, 54:159–178.
[26] Elliott G, Rothenberg T J, Stock J H. Efficient Tests for an Autoregressive UnitRoot[J]. Econometrica, 1996, 64(4):813–836.
[27] Banerjee J, A.and Dolado, Galbraith J, Hendry D. Cointegration, Error Correc-tion, and the Econometric Analysis of Non-Stationary Data[M]. Oxford: OxfordUniversity Press, 1993.
[28] Ng S, Perron P. Unit Root Tests in ARMA Models with Data-Dependent Methodsfor the Selection of the Truncation Lag[J]. Journal of the American StatisticalAssociation, 1995, 90(429):268–281.
[29] Nelsen R. An Introduction to Copulas[M]. Berlin: Springer, 1998.
[30] Ledford AW, Tawn J A. Diagnostics for dependence within time-series extremes.J. R. Statist. Soc. B[J]. 2003, 65(2):521–543.
[31] Heffernan J E. A directory of coefficients of tail dependence[J]. Extremes, 2000,3(3):279–290.
[32] ThodeJr H C. Testing for Normality[M]. New York.: Marcel Dekker, 2002.
[33]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, 20(2):216–219.
[34]王春峰,程鹏飞,房振明.中国股市流动性与波动性关系的实证研究[J].北京理工大学学报：社会科学版, 2007, 9(4):63–66.
[35]王春峰,韩冬,蒋祥林.基于信息非对称模型的交易行为与波动性关系研究――交易规模和交易频率[J].管理工程学报, 2007, 21(1):134–137.
[36]王春峰.基于时间特性的中国股市交易集群性特征的研究[J].管理工程学报, 2006, 20(2):28–33.
[37]房振明,王春峰.交易频率视角下我国股市量价关系研究[J].系统工程学报,2007, 22(4):386–393.
[38] Mandelbrot B. The variation of certain speculative prices[J]. Journal of Business,1963, 36:394–419.
[39] Mandelbrot B, Taylo H. On the distribution of stock price differences[J]. OperationsResearch, 1967, 15:1057–1062.
[40] Engle R. Autorregressive Conditional Heteroskedasticity with Estimates ofUnited Kingdom Inflation[J]. Econometrica, 1982, 50:987–1008.
[41]罗登跃,王春峰.上证指数收益率、波动性与成交量动态关系研究――基于日数据的非线性动力学实证分析[J].系统工程理论与实践, 2005,25(7):41–48.
[42] Bali R, Guirguis H. Extreme observations and non-normality in ARCHand GARCH[J]. International Review of Economics & Finance, 2007,16(3):332–346. http://www.sciencedirect.com/science/article/B6W4V-4GTWRXJ-1/2/14b9898ade95a044629472add9652627.
[43] Bellini F, Bottolo L. Stationarity domains for [delta]-power Garchprocess with heavy tails[J]. Statistics & Probability Letters, 2007,77(13):1418–1427. http://www.sciencedirect.com/science/article/B6V1D-4N7RXXG-1/2/7e77101c4b92132c193ce18671958c50.
[44] Cook S. The impact of GARCH on asymmetric unit root tests[J]. PhysicaA: Statistical Mechanics and its Applications, 2006, 369(2):745–752. http://www.sciencedirect.com/science/article/B6TVG-4JG469P-1/2/3d9972fde8e4959e1f2b915550fcecd5.
[45] Christian F, Jean-Michel Z. Deriving the autocovariances of powers ofMarkov-switching GARCH models, with applications to statistical infer-ence[J]. Computational Statistics & Data Analysis, 2007, In Press, Cor-rected Proof:–873. http://www.sciencedirect.com/science/article/B6V8V-4PFDDH8-1/2/40dbf27a0182b740da3120b2a0d6ba92.
[46] Gerlach R, Tuyl F. MCMC methods for comparing stochastic volatil-ity and GARCH models[J]. International Journal of Forecasting, 2006,22(1):91–107. http://www.sciencedirect.com/science/article/B6V92-4H2PJBV-1/2/0c03cb6348b57ca8721d31035a4394bb.
[47] Hang Chan N, Deng S J, Peng L, et al. Interval estimation of value-at-risk basedon GARCH models with heavy-tailed innovations[J]. Journal of Economet-rics, 2007, 137(2):556–576. http://www.sciencedirect.com/science/article/B6VC0-4K428TS-1/2/681030b83d7568444c054fdd9a37b96b.
[48] Jondeau E, Rockinger M. The Copula-GARCH model of conditionaldependencies: An international stock market application[J]. Journalof International Money and Finance, 2006, 25(5):827–853. http://www.sciencedirect.com/science/article/B6V9S-4KKWVGS-1/2/57f131fc1071f08e2fc7c7bf248fc0b3.
[49] Ling S. Self-weighted and local quasi-maximum likelihood estimatorsfor ARMA-GARCH/IGARCH models[J]. Journal of Econometrics, 2007,140(2):849–873. http://www.sciencedirect.com/science/article/B6VC0-4KST3TB-1/2/99de2f1e3c8a6f82c93ac2facf8e9f7a.
[50] Liu J C. Stationarity for a Markov-switching Box-Cox transformedthreshold GARCH process[J]. Statistics & Probability Letters, 2007,77(13):1428–1438. http://www.sciencedirect.com/science/article/B6V1D-4N7SBJM-4/2/6aaae718ad7332bc247ea7146b205032.
[51] Pascual L, Romo J, Ruiz E. Bootstrap prediction for returns and volatilitiesin GARCH models[J]. Computational Statistics & Data Analysis, 2006,50(9):2293–2312. http://www.sciencedirect.com/science/article/B6V8V-4F8TG43-2/2/c4d2784d05693220bc5b0d1a47a6c398.
[52] Sohn S Y, Lim M. Hierarchical forecasting based on AR-GARCH modelin a coherent structure[J]. European Journal of Operational Research, 2007,176(2):1033–1040. http://www.sciencedirect.com/science/article/B6VCT-4HK5SPP-8/2/e0831db21fa98a43703461aec497f42b.
[53] Wen Cheong C, Hassan Shaari Mohd Nor A, Isa Z. Asymmetry andlong-memory volatility: Some empirical evidence using GARCH[J]. PhysicaA: Statistical and Theoretical Physics, 2007, 373:651–664. http://www.sciencedirect.com/science/article/B6TVG-4K8YD7J-1/2/736b1d1976cb5cdb6496e67ecc7d081a.
[54] de Wet W. A structural GARCH model: An application on SouthAfrican data[J]. Economic Modelling, 2006, 23(5):775–791. http://www.sciencedirect.com/science/article/B6VB1-4KHC3DT-1/2/40fd6b7d0fb9a6bdee175685d6a8edf6.
[55] Wong K F K, Galka A, Yamashita O, et al. Modelling non-stationaryvariance in EEG time series by state space GARCH model[J]. Computersin Biology and Medicine, 2006, 36(12):1327–1335. http://www.sciencedirect.com/science/article/B6T5N-4HK04PV-2/2/f28fd83f883a7145342eb4d2b1b41667.
[56] Yang J P, Cheng S H, Zhang L H. Bivariate copula decomposition in terms ofcomonotonicity, countermonotonicity and independence[J]. Insurance Mathematics& Economics, 2006, 39(2):267–284.
[57]王春峰,张蕊,房振明, et al.高频数据下投资组合风险预测模型比较[J].系统工程, 2007, 25(3):23–28.
[58]刘志东,徐淼.基于GARCH和EVT的金融资产风险价值度量方法[J].统计与决策, 2007(18):13–16.
[59]周颖,仇晓光.基于CVaR―GARCH―GED模型的单品种期货风险价值预测[J].统计与决策, 2007(18):95–97.
[60]苏岩,杨振海. GARCH（1,1）模型及其在汇率条件波动预测中的应用[J].数理统计与管理, 2007, 26(4):615–620.
[61]张跃军,范英,魏一鸣.基于GED-GARCH模型的中国原油价格波动特征研究[J].数理统计与管理, 2007, 26(3):398–406.
[62]杨立洪,徐黄玮,曹显兵.可转换债券风险测度的新方法――GAVaR模型[J].数学的实践与认识, 2007, 37(11):92–98.
[63]刘达,牛东晓,邢棉,等.基于GARCH误差校正的遗传支持向量机日前电价预测[J].电力系统自动化, 2007, 31(11):31–34,58.
[64] Bollerslev T. Generalized Autorregressive Conditional Heteroskedasticity[J].Journal of Econometrics, 1986, 31:307–327.
[65] Taylor S. Modelling Financial Time Series[M]. New York: Wiley, 1986.
[66] Nelson D B. onditional heteroskedasticity in asset returns: A new approach[J].Econometrica, 1991, 59:347–370.
[67] Schwert G W. Stock Volatility and the Crash of 87[J]. The Review of FinancialStudies, 1990, 3:77–102.
[68] Ding Z, Granger C W J, Engle R F. A long memory property ofstock market returns and a new model[J]. Journal of Empirical Finance,1993, 1(1):83–106. http://www.sciencedirect.com/science/article/B6VFG-45JK6Y4-6/2/eee18eb183d6659d1228a632c3d2c9f4.
[69] Engle R F, Ng V. Measuring and Testing the Impact of News on Volatility[J].Journal of Finance, 1993, 45:1749–1777.
[70] Glosten L, Jagannathan R, Runkle D. On the Relation Between the ExpectedValue and the Volatility on the Nominal Excess Returns on Stocks[J]. Journal ofFinance, 1993, 48:1779–1801.
[71] Duan J C. Augmented GARCH(p,q) process and its diffusion limit[J]. Journalof Econometrics, 1997, 79(1):97–127. http://www.scopus.com/scopus/inward/record.url?eid=2-s2.0-0002229006&partnerID=40&rel=R7.0.0.
[72] Milhoj A. The moment structure of ARCH models[J]. Scandinavian Journal ofStatistics, 1985, 12:281–292.
[73] Zakoian J. Threshold Heteroskedastic Models[J]. Journal of Economic Dynamicsand Control, 1994, 18:931–955.
[74] Hentschel L. All in the family Nesting symmetric and asymmetric GARCHmodels[J]. Journal of Financial Economics, 1995, 39(1):71–104. available athttp://ideas.repec.org/a/eee/jfinec/v39y1995i1p71-104.html.
[75] Engle R. Dynamic Conditional Correlation: A Simple Class of MultivariateGeneralized Autoregressive Conditional Heteroskedasticity Mod-els[J]. Journal of Business & Economic Statistics, 2002, 20:339–350(12). http://www.ingentaconnect.com/content/asa/jbes/2002/00000020/00000003/art00002.
[76] Bollerslev T. Modelling the Coherence in Short Run Nominal Exchange Rates: AMultivariate Generalized ARCH Model[J]. Review of Economics and Statistics,1990, 72(3):498–505.
[77] Glosten R, L.and Jagannathan, Runkle D. Relationship between the expectedvalue and the volatility of the nominal excess return on stocks[R]. ColumbiaUniversity: Department of Finance, 1989.
[78] Kon S J. Models of stock returns: a comparison[J]. Journal of Finance, 1984,39:147–165.
[79] Blattberg R, Gonedes N. A comparison of the stable and student distributions asstatistical models for stock prices[J]. Journal of Business, 1974, 47:244–280.
[80] Bollerslev T, Chou R Y, Kroner K F. ARCH modeling in finance : A review of thetheory and empirical evidence[J]. Journal of Econometrics, 1992, 52(1-2):5–59.available at http://ideas.repec.org/a/eee/econom/v52y1992i1-2p5-59.html.
[81] Pickands J. Statistical inference using extreme order statistics[J]. The Annals ofStatistics, 1975, 3(1):119–131.
[82] Leadbetter M R. On a basis for peaks over threshold modeling[J]. Statistics andProbability Letters, 1991, 12(4):357–362.
[83] Beirlant J, Vynckier P, Teugels J L. Tail Index Estimation, Pareto Quantile Plots,and Regression Diagnostics[J]. Journal of the American Statistical Association,1996, 91:1659–1667.
[84] Durrleman E A, Nikeghbali A. Copulas for Finance: A Reading Guide and SomeApplications[R]. London: Working Paper of City University Business School,2000.
[85] Chen X H, Fan Y Q. Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification[J]. Journal ofEconometrics, 2006, 135(1-2):125–154.
[86] Chen X H, Fan Y Q, Tsyrennikov V. E?cient estimation of semiparametricmultivariate copula models[J]. Journal of the American Statistical Association,2006, 101(475):1228–1240.
[87] Grimaldi S, Serinaldi F. Asymmetric copula in multivariate ?ood frequency anal-ysis[J]. Advances in Water Resources, 2006, 29(8):1155–1167.
[88] Jaworski P. On value at risk for foreign exchange ratesThe copula approach[J].Acta Physica Polonica B, 2006, 37(11):3005–3015.
[89] Pitt M, Chan D, Kohn R. Efficient Bayesian inference for Gaussian copula regressionmodels[J]. Biometrika, 2006, 93(3):537–554.
[90] Shen C Y, Weissfeld L. A copula model for repeated measurements with nonignorablenon-monotone missing outcome[J]. Statistics In Medicine, 2006,25(14):2427–2440.
[91]罗俊鹏. Copula理论及其金融分析中的应用研究[D].天津:天津大学, 2006.
[92]韦艳华. copula理论及其在多变量金融时间序列分析上的应用研究[D].天津:天津大学, 2004.
[93]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, 16(3):302–306.
[94] Fang B Q. The skew elliptical distributions and their quadratic forms[J]. Journalof Multivariate Analysis, 2003, 87:298–314.
[95] Gabriel F, Markus J, Alexander S. Elliptical copulas: applicability and limitations[J]. Statistics and Probability Letters, 2003, 63:275–286.
[96] Krassimir R. Non-parametric Estimation of Elliptical CopulaeWith Applicationto Credit Risk[R].[S.l.]: Working paper, 2002.
[97] Schott J. Testing for elliptical symmetry in covariance-matrix-based analyses[J].Statistics and Probability Letters, 2002, 60:395–404.
[98] Genest L, C.and Rivest. Statistical inference procedures for bivariatearchimedean copulas[J]. Journal of American Statistic Association, 1993,88:1034–1043.
[99] Widder D. The Laplace Transform[M]. Princeton: Princeton University Press,1941.
[100] Barbe P, Genest C, Ghoudi K, et al. On Kendall’s process[J]. Journal of MultivariateAnalysis, 1996, 58:197–229.
[101]韦艳华,张世英,郭焱.金融市场相关程度与相关模式的研究[J].系统工程学报, 2004, 19(4):355–362.
[102]史道济.二元极值分布参数的最大似然估计与分步估计[J].天津大学学报,1994, 27:294–299.
[103] Genest C. Frank’s family of bivariate distributions[J]. Biometrika, 1987,74(3):549–555.
[104] Oakes D. Semiparametric inference in a model for association in bivariate sur-vival data[J]. Biometrika, 1986, 73(2):353–361.
[105] Hougaard P. Fitting a multivariate failure time distribution[J]. IEEE TRANSACTIONSON RELIABILITY, 1989, 38:444–448.
[106] Clayton D, Cuzick J. Multivariate generalizations of the proportional hazardsmodel (with discussion)[J]. Journal of the Royal Statistical Society: Series A,1985, 2:82–117.
[107] Genest C, Ghoudi K, Rivest L. A semiparametric estimation procedure of dependenceparameters in multivariate families of distributions[J]. Biometrika, 1995,82(3):543–552.
[108] Klaassen C A J, Wellner J A. Efficient estimation in the bivariate normal copulamodel: normal margins are least favourable[J]. Bernoulli, 1997, 3(1):55–77.
[109] Genest C, Werker B. Conditions for the asymptotic semiparametric effciencyof an omnibus estimator of dependence parameters in copula models[C]//Proceedings of the Conference on Distributions with Given Marginalsand Statistical Modelling. .[S.l.]: [s.n.] , 2002.
[110]史道济,姚庆祝.改进Copula对数据拟合的方法[J].系统工程理论与实践,2004, 22(9):42–45.
[111] Wang W, Wells M T. Model selection and semiparametric inference for bivariatefailure-time data[J]. Journal of The American Statistical Association, 2000,95:62–72.
[112] Fermanian J. Goodness of fit tests for copulas[J]. Journal of Multivariate Analysis,2005, 95:119–152.
[113] Cornelia S, Mark T. Goodness-of-fit Tests for Parametric Families ofArchimedean Copulas[R]. Münster: University of Muenster, 2004.
[114] Bickel P, Rosenblatt M. On some global meansures of the deviation of densityfunction estimates[J]. Annals of Statistics, 1973, 1:1071–1095.
[115] Joe H. Multivariate models and dependence concepts[M]. London: Chapmanand Hall, 1999.
[116]梁冯珍,钟君,史道济.尾部相关性对投资组合VaR的影响分析[J].系统工程理论与实践, 2007, 27(7):64–68.
[117] Sibuya M. Bivariate extreme statistics.[J]. Annals of the Institute of StatisticalMathematics, 1960(11):195–210.
[118] Coles J, S.G.and Heffernan, Tawn J A. Dependence measures for multivariateextremes[J]. Extremes, 1999, 2:339–365.
[119]史道济,孙炳堃.二元Cauchy分布尾部的相关性[J].天津大学学报, 2000,33(4):432–434.
[120] Mari D D, Kotz s. Correlation and Dependence[M]. London: Imperial CollegePress, 2001.
[121] R Development Core Team. R: A Language and Environment for StatisticalComputing[H]. R Foundation for Statistical Computing, Vienna, Austria, 2006.http://www.R-project.org. ISBN 3-900051-07-0.
[122] Embrechts P, Lindskog F, McNeil A J. Modelling dependence with copulas andapplications to risk management[M]. Amserdam: Elsevier/North-Holland, 2003.
[123] Matsumoto M, Nishimura T. Mersenne Twister: A 623-dimensionally equidistributeduniform pseudo-random number generator[J]. ACM Transactions onModeling and Computer Simulation, 1998, 8:3–30.
[124] Fishburm P C, Wakker P. The invention of the independence condition for preferences[J]. Management Science, 1995, 41:1130–1144.
[125]王春峰. VaR金融市场风险管理[M].天津:天津大学出版社, 2001.
[126] Dowd K, Cairns A, Blake D. Mortality-dependent financial risk measures[J].Insurance Mathematics & Economics, 2006, 38(3):427– 40. http://dx.doi.org/10.1016/j.insmatheco.2005.11.003.
[127] Ren W, Jin-cheng S, Yang F, et al. Combined bidding strategy and model forpower suppliers based on CVaR risk measurement techniques[J]. Automation ofElectric Power Systems, 2005, 29(14):5– 9.
[128] Delbaen F. Coherent risk measures on general probability spaces[M]. Berlin:Springer-Verlag, 2002.
[129] Boda K, Filar J. Time consistent dynamic risk measures[J]. Mathematical Methodsof Operations Research, 2006, 63(1):169– 86. http://dx.doi.org/10.1007/s00186-005-0045-1.
[130] Sakalauskas V, Kriksciuniene D. Short-term investment risk measurement usingVaR and CVaR[J]. Computational Science-ICCS 2006. 6th International Conference.Proceedings, Part IV (Lecture Notes in Computer Science Vol.3994),2006:316– 23.
[131] Cheng S, Liu Y,Wang S. Progress in Risk Measurement[J]. Advanced Modellingand Optimization, 2004, 6:1–20.
[2] International Institute for Urban Development of Beijin . China City LivingQuality Report No.1[R].[S.l.]: 2006 China City Forum Beijing Summ, 2006.
[3] Malpezzi S. A simple error correction model of housing prices[J]. Journal ofHousing Economics, 1999, 8(1):27–62.
[4] Seko M. Housing prices and economic cycles[C]//The International ConferenceonHousingMarket and the Macro Economy. Hong Kong: [s.n.] , 2003.
[5] Anglin P. Local dynamics and contagion in real estate markets[C]//The InternationalConference on Real Estates and Macro Economy. Beijing: [s.n.] , 2006.
[6] Liu J G, Zhang X L, Wu W P. Application of fuzzy neural network for realestate prediction[J]. ADVANCES IN NEURAL NETWORKSISNN 2006, PT 3,PROCEEDINGS, 2006, 3973:1187–1191.
[7] Zhou W X, Sornette D. Analysis of the real estate market in Las Vegas:Bubble, seasonal patterns, and prediction of the CSW indices[J]. Physica A:Statistical Mechanics and its Applications, 2008, 387(1):243– 260. http://dx.doi.org/10.1016/j.physa.2007.08.059. Econophysics;Real estatemarket;Power law;.
[8] Wedyawati W, Lu M. Mining real estate listings using ORACLE data warehousingand predictive regression[C]//. United States: Las Vegas, NV, 2004:296–301. Predictive data mining;Regression;Real estate multiple listing service;Datamining technology;.
[9] Bin O. A prediction comparison of housing sales prices by parametricversus semi-parametric regressions[J]. Journal of Housing Economics,2004, 13(1):68–84. http://www.sciencedirect.com/science/article/B6WJR-4BSVPMJ-1/2/65ed4dc9c7eefc532ca702230156be0f.
[10] Case B, Clapp J, Dubin R, et al. Modeling Spatial and Temporal House Price Patterns:A Comparison of Four Models[J]. The Journal of Real Estate Finance andEconomics, 2004, 29(2):167–191. http://dx.doi.org/10.1023/B:REAL.0000035309.60607.53.
[11] Clapp J M, Giaccotto C. Evaluating House Price Forecasts[J].Journal of Real Estate Research, 2002, 24(1):1–26. available athttp://ideas.repec.org/a/jre/issued/v24n12002p1-26.html.
[12]王婧,田澎.小波神经网络在房地产价格指数预测中的应用[J].计算机仿真,2005(7):96–98.
[13]杨楠,邢力聪.灰色马尔可夫模型在房价指数预测中的应用[J].统计与信息论坛, 2006, 21(5):52–55.
[14]龙会典,张海燕.基于ARIMA模型的广州市商品房价格预测[J].商业研究,2007(7):211–213.
[15]李岳,黄河,王启星,等.国内平均房价增长的极限[J].统计与决策,2003(6):56–56.
[16] Pollatsek A, Tversky A N. A theory of risk[J]. Journal of Mathematical Psychology,1970, 7:540–553.
[17] Ramsay C M. Loading gross premiums for risk without using utility theory(withDiscussions)[J]. Transactions of the Society of Actuaries XLV, 1994, 48:305–349.
[18] Artzner P, Delbaen J M, F. adn Eber, Heath D. Coherent measure of risk[J].Mathematical Finance, 1999, 9:203–208.
[19]王爱民,何 信.金融风险统计度量标准研究[J].统计研究, 2005(2):67–71.
[20] Brock D W, W.A., Scheinkman J. A test for independence based on the correlationdimension[R].[S.l.]: University of Wisconsin-Madison and University ofChicago, 1986.
[21] Theiler J, Eubank S, Longtin A, et al. Testing for nonlinearity in time series: themethod of surrogate data[J]. Physica D Nonlinear Phenomena, 1992, 58:77–94.
[22] Dickey D, Fuller W. Distribution of the estimators for autoregressive time serieswith a unit root[J]. Journal of the American Statistical Association, 1979,74:427–431.
[23] Said S E, Dickey D A. Testing for Unit Roots in Autoregressive-Moving AverageModels of Unknown Order[J]. Biometrika, 1984, 71:599–607.
[24] Perron P. Trends and Random Walks in Macroeconomic Time Series[J]. Journalof Economic Dynamics and Control, 1988, 12:297–332.
[25] Kwiatkowski D, Phillips P C B, Schmidt P, et al. Testing the Null Hypothesis ofStationarity against the Alternative of a Unit Root[J]. Journal of Econometrics,1992, 54:159–178.
[26] Elliott G, Rothenberg T J, Stock J H. Efficient Tests for an Autoregressive UnitRoot[J]. Econometrica, 1996, 64(4):813–836.
[27] Banerjee J, A.and Dolado, Galbraith J, Hendry D. Cointegration, Error Correc-tion, and the Econometric Analysis of Non-Stationary Data[M]. Oxford: OxfordUniversity Press, 1993.
[28] Ng S, Perron P. Unit Root Tests in ARMA Models with Data-Dependent Methodsfor the Selection of the Truncation Lag[J]. Journal of the American StatisticalAssociation, 1995, 90(429):268–281.
[29] Nelsen R. An Introduction to Copulas[M]. Berlin: Springer, 1998.
[30] Ledford AW, Tawn J A. Diagnostics for dependence within time-series extremes.J. R. Statist. Soc. B[J]. 2003, 65(2):521–543.
[31] Heffernan J E. A directory of coefficients of tail dependence[J]. Extremes, 2000,3(3):279–290.
[32] ThodeJr H C. Testing for Normality[M]. New York.: Marcel Dekker, 2002.
[33]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, 20(2):216–219.
[34]王春峰,程鹏飞,房振明.中国股市流动性与波动性关系的实证研究[J].北京理工大学学报：社会科学版, 2007, 9(4):63–66.
[35]王春峰,韩冬,蒋祥林.基于信息非对称模型的交易行为与波动性关系研究――交易规模和交易频率[J].管理工程学报, 2007, 21(1):134–137.
[36]王春峰.基于时间特性的中国股市交易集群性特征的研究[J].管理工程学报, 2006, 20(2):28–33.
[37]房振明,王春峰.交易频率视角下我国股市量价关系研究[J].系统工程学报,2007, 22(4):386–393.
[38] Mandelbrot B. The variation of certain speculative prices[J]. Journal of Business,1963, 36:394–419.
[39] Mandelbrot B, Taylo H. On the distribution of stock price differences[J]. OperationsResearch, 1967, 15:1057–1062.
[40] Engle R. Autorregressive Conditional Heteroskedasticity with Estimates ofUnited Kingdom Inflation[J]. Econometrica, 1982, 50:987–1008.
[41]罗登跃,王春峰.上证指数收益率、波动性与成交量动态关系研究――基于日数据的非线性动力学实证分析[J].系统工程理论与实践, 2005,25(7):41–48.
[42] Bali R, Guirguis H. Extreme observations and non-normality in ARCHand GARCH[J]. International Review of Economics & Finance, 2007,16(3):332–346. http://www.sciencedirect.com/science/article/B6W4V-4GTWRXJ-1/2/14b9898ade95a044629472add9652627.
[43] Bellini F, Bottolo L. Stationarity domains for [delta]-power Garchprocess with heavy tails[J]. Statistics & Probability Letters, 2007,77(13):1418–1427. http://www.sciencedirect.com/science/article/B6V1D-4N7RXXG-1/2/7e77101c4b92132c193ce18671958c50.
[44] Cook S. The impact of GARCH on asymmetric unit root tests[J]. PhysicaA: Statistical Mechanics and its Applications, 2006, 369(2):745–752. http://www.sciencedirect.com/science/article/B6TVG-4JG469P-1/2/3d9972fde8e4959e1f2b915550fcecd5.
[45] Christian F, Jean-Michel Z. Deriving the autocovariances of powers ofMarkov-switching GARCH models, with applications to statistical infer-ence[J]. Computational Statistics & Data Analysis, 2007, In Press, Cor-rected Proof:–873. http://www.sciencedirect.com/science/article/B6V8V-4PFDDH8-1/2/40dbf27a0182b740da3120b2a0d6ba92.
[46] Gerlach R, Tuyl F. MCMC methods for comparing stochastic volatil-ity and GARCH models[J]. International Journal of Forecasting, 2006,22(1):91–107. http://www.sciencedirect.com/science/article/B6V92-4H2PJBV-1/2/0c03cb6348b57ca8721d31035a4394bb.
[47] Hang Chan N, Deng S J, Peng L, et al. Interval estimation of value-at-risk basedon GARCH models with heavy-tailed innovations[J]. Journal of Economet-rics, 2007, 137(2):556–576. http://www.sciencedirect.com/science/article/B6VC0-4K428TS-1/2/681030b83d7568444c054fdd9a37b96b.
[48] Jondeau E, Rockinger M. The Copula-GARCH model of conditionaldependencies: An international stock market application[J]. Journalof International Money and Finance, 2006, 25(5):827–853. http://www.sciencedirect.com/science/article/B6V9S-4KKWVGS-1/2/57f131fc1071f08e2fc7c7bf248fc0b3.
[49] Ling S. Self-weighted and local quasi-maximum likelihood estimatorsfor ARMA-GARCH/IGARCH models[J]. Journal of Econometrics, 2007,140(2):849–873. http://www.sciencedirect.com/science/article/B6VC0-4KST3TB-1/2/99de2f1e3c8a6f82c93ac2facf8e9f7a.
[50] Liu J C. Stationarity for a Markov-switching Box-Cox transformedthreshold GARCH process[J]. Statistics & Probability Letters, 2007,77(13):1428–1438. http://www.sciencedirect.com/science/article/B6V1D-4N7SBJM-4/2/6aaae718ad7332bc247ea7146b205032.
[51] Pascual L, Romo J, Ruiz E. Bootstrap prediction for returns and volatilitiesin GARCH models[J]. Computational Statistics & Data Analysis, 2006,50(9):2293–2312. http://www.sciencedirect.com/science/article/B6V8V-4F8TG43-2/2/c4d2784d05693220bc5b0d1a47a6c398.
[52] Sohn S Y, Lim M. Hierarchical forecasting based on AR-GARCH modelin a coherent structure[J]. European Journal of Operational Research, 2007,176(2):1033–1040. http://www.sciencedirect.com/science/article/B6VCT-4HK5SPP-8/2/e0831db21fa98a43703461aec497f42b.
[53] Wen Cheong C, Hassan Shaari Mohd Nor A, Isa Z. Asymmetry andlong-memory volatility: Some empirical evidence using GARCH[J]. PhysicaA: Statistical and Theoretical Physics, 2007, 373:651–664. http://www.sciencedirect.com/science/article/B6TVG-4K8YD7J-1/2/736b1d1976cb5cdb6496e67ecc7d081a.
[54] de Wet W. A structural GARCH model: An application on SouthAfrican data[J]. Economic Modelling, 2006, 23(5):775–791. http://www.sciencedirect.com/science/article/B6VB1-4KHC3DT-1/2/40fd6b7d0fb9a6bdee175685d6a8edf6.
[55] Wong K F K, Galka A, Yamashita O, et al. Modelling non-stationaryvariance in EEG time series by state space GARCH model[J]. Computersin Biology and Medicine, 2006, 36(12):1327–1335. http://www.sciencedirect.com/science/article/B6T5N-4HK04PV-2/2/f28fd83f883a7145342eb4d2b1b41667.
[56] Yang J P, Cheng S H, Zhang L H. Bivariate copula decomposition in terms ofcomonotonicity, countermonotonicity and independence[J]. Insurance Mathematics& Economics, 2006, 39(2):267–284.
[57]王春峰,张蕊,房振明, et al.高频数据下投资组合风险预测模型比较[J].系统工程, 2007, 25(3):23–28.
[58]刘志东,徐淼.基于GARCH和EVT的金融资产风险价值度量方法[J].统计与决策, 2007(18):13–16.
[59]周颖,仇晓光.基于CVaR―GARCH―GED模型的单品种期货风险价值预测[J].统计与决策, 2007(18):95–97.
[60]苏岩,杨振海. GARCH（1,1）模型及其在汇率条件波动预测中的应用[J].数理统计与管理, 2007, 26(4):615–620.
[61]张跃军,范英,魏一鸣.基于GED-GARCH模型的中国原油价格波动特征研究[J].数理统计与管理, 2007, 26(3):398–406.
[62]杨立洪,徐黄玮,曹显兵.可转换债券风险测度的新方法――GAVaR模型[J].数学的实践与认识, 2007, 37(11):92–98.
[63]刘达,牛东晓,邢棉,等.基于GARCH误差校正的遗传支持向量机日前电价预测[J].电力系统自动化, 2007, 31(11):31–34,58.
[64] Bollerslev T. Generalized Autorregressive Conditional Heteroskedasticity[J].Journal of Econometrics, 1986, 31:307–327.
[65] Taylor S. Modelling Financial Time Series[M]. New York: Wiley, 1986.
[66] Nelson D B. onditional heteroskedasticity in asset returns: A new approach[J].Econometrica, 1991, 59:347–370.
[67] Schwert G W. Stock Volatility and the Crash of 87[J]. The Review of FinancialStudies, 1990, 3:77–102.
[68] Ding Z, Granger C W J, Engle R F. A long memory property ofstock market returns and a new model[J]. Journal of Empirical Finance,1993, 1(1):83–106. http://www.sciencedirect.com/science/article/B6VFG-45JK6Y4-6/2/eee18eb183d6659d1228a632c3d2c9f4.
[69] Engle R F, Ng V. Measuring and Testing the Impact of News on Volatility[J].Journal of Finance, 1993, 45:1749–1777.
[70] Glosten L, Jagannathan R, Runkle D. On the Relation Between the ExpectedValue and the Volatility on the Nominal Excess Returns on Stocks[J]. Journal ofFinance, 1993, 48:1779–1801.
[71] Duan J C. Augmented GARCH(p,q) process and its diffusion limit[J]. Journalof Econometrics, 1997, 79(1):97–127. http://www.scopus.com/scopus/inward/record.url?eid=2-s2.0-0002229006&partnerID=40&rel=R7.0.0.
[72] Milhoj A. The moment structure of ARCH models[J]. Scandinavian Journal ofStatistics, 1985, 12:281–292.
[73] Zakoian J. Threshold Heteroskedastic Models[J]. Journal of Economic Dynamicsand Control, 1994, 18:931–955.
[74] Hentschel L. All in the family Nesting symmetric and asymmetric GARCHmodels[J]. Journal of Financial Economics, 1995, 39(1):71–104. available athttp://ideas.repec.org/a/eee/jfinec/v39y1995i1p71-104.html.
[75] Engle R. Dynamic Conditional Correlation: A Simple Class of MultivariateGeneralized Autoregressive Conditional Heteroskedasticity Mod-els[J]. Journal of Business & Economic Statistics, 2002, 20:339–350(12). http://www.ingentaconnect.com/content/asa/jbes/2002/00000020/00000003/art00002.
[76] Bollerslev T. Modelling the Coherence in Short Run Nominal Exchange Rates: AMultivariate Generalized ARCH Model[J]. Review of Economics and Statistics,1990, 72(3):498–505.
[77] Glosten R, L.and Jagannathan, Runkle D. Relationship between the expectedvalue and the volatility of the nominal excess return on stocks[R]. ColumbiaUniversity: Department of Finance, 1989.
[78] Kon S J. Models of stock returns: a comparison[J]. Journal of Finance, 1984,39:147–165.
[79] Blattberg R, Gonedes N. A comparison of the stable and student distributions asstatistical models for stock prices[J]. Journal of Business, 1974, 47:244–280.
[80] Bollerslev T, Chou R Y, Kroner K F. ARCH modeling in finance : A review of thetheory and empirical evidence[J]. Journal of Econometrics, 1992, 52(1-2):5–59.available at http://ideas.repec.org/a/eee/econom/v52y1992i1-2p5-59.html.
[81] Pickands J. Statistical inference using extreme order statistics[J]. The Annals ofStatistics, 1975, 3(1):119–131.
[82] Leadbetter M R. On a basis for peaks over threshold modeling[J]. Statistics andProbability Letters, 1991, 12(4):357–362.
[83] Beirlant J, Vynckier P, Teugels J L. Tail Index Estimation, Pareto Quantile Plots,and Regression Diagnostics[J]. Journal of the American Statistical Association,1996, 91:1659–1667.
[84] Durrleman E A, Nikeghbali A. Copulas for Finance: A Reading Guide and SomeApplications[R]. London: Working Paper of City University Business School,2000.
[85] Chen X H, Fan Y Q. Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification[J]. Journal ofEconometrics, 2006, 135(1-2):125–154.
[86] Chen X H, Fan Y Q, Tsyrennikov V. E?cient estimation of semiparametricmultivariate copula models[J]. Journal of the American Statistical Association,2006, 101(475):1228–1240.
[87] Grimaldi S, Serinaldi F. Asymmetric copula in multivariate ?ood frequency anal-ysis[J]. Advances in Water Resources, 2006, 29(8):1155–1167.
[88] Jaworski P. On value at risk for foreign exchange ratesThe copula approach[J].Acta Physica Polonica B, 2006, 37(11):3005–3015.
[89] Pitt M, Chan D, Kohn R. Efficient Bayesian inference for Gaussian copula regressionmodels[J]. Biometrika, 2006, 93(3):537–554.
[90] Shen C Y, Weissfeld L. A copula model for repeated measurements with nonignorablenon-monotone missing outcome[J]. Statistics In Medicine, 2006,25(14):2427–2440.
[91]罗俊鹏. Copula理论及其金融分析中的应用研究[D].天津:天津大学, 2006.
[92]韦艳华. copula理论及其在多变量金融时间序列分析上的应用研究[D].天津:天津大学, 2004.
[93]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, 16(3):302–306.
[94] Fang B Q. The skew elliptical distributions and their quadratic forms[J]. Journalof Multivariate Analysis, 2003, 87:298–314.
[95] Gabriel F, Markus J, Alexander S. Elliptical copulas: applicability and limitations[J]. Statistics and Probability Letters, 2003, 63:275–286.
[96] Krassimir R. Non-parametric Estimation of Elliptical CopulaeWith Applicationto Credit Risk[R].[S.l.]: Working paper, 2002.
[97] Schott J. Testing for elliptical symmetry in covariance-matrix-based analyses[J].Statistics and Probability Letters, 2002, 60:395–404.
[98] Genest L, C.and Rivest. Statistical inference procedures for bivariatearchimedean copulas[J]. Journal of American Statistic Association, 1993,88:1034–1043.
[99] Widder D. The Laplace Transform[M]. Princeton: Princeton University Press,1941.
[100] Barbe P, Genest C, Ghoudi K, et al. On Kendall’s process[J]. Journal of MultivariateAnalysis, 1996, 58:197–229.
[101]韦艳华,张世英,郭焱.金融市场相关程度与相关模式的研究[J].系统工程学报, 2004, 19(4):355–362.
[102]史道济.二元极值分布参数的最大似然估计与分步估计[J].天津大学学报,1994, 27:294–299.
[103] Genest C. Frank’s family of bivariate distributions[J]. Biometrika, 1987,74(3):549–555.
[104] Oakes D. Semiparametric inference in a model for association in bivariate sur-vival data[J]. Biometrika, 1986, 73(2):353–361.
[105] Hougaard P. Fitting a multivariate failure time distribution[J]. IEEE TRANSACTIONSON RELIABILITY, 1989, 38:444–448.
[106] Clayton D, Cuzick J. Multivariate generalizations of the proportional hazardsmodel (with discussion)[J]. Journal of the Royal Statistical Society: Series A,1985, 2:82–117.
[107] Genest C, Ghoudi K, Rivest L. A semiparametric estimation procedure of dependenceparameters in multivariate families of distributions[J]. Biometrika, 1995,82(3):543–552.
[108] Klaassen C A J, Wellner J A. Efficient estimation in the bivariate normal copulamodel: normal margins are least favourable[J]. Bernoulli, 1997, 3(1):55–77.
[109] Genest C, Werker B. Conditions for the asymptotic semiparametric effciencyof an omnibus estimator of dependence parameters in copula models[C]//Proceedings of the Conference on Distributions with Given Marginalsand Statistical Modelling. .[S.l.]: [s.n.] , 2002.
[110]史道济,姚庆祝.改进Copula对数据拟合的方法[J].系统工程理论与实践,2004, 22(9):42–45.
[111] Wang W, Wells M T. Model selection and semiparametric inference for bivariatefailure-time data[J]. Journal of The American Statistical Association, 2000,95:62–72.
[112] Fermanian J. Goodness of fit tests for copulas[J]. Journal of Multivariate Analysis,2005, 95:119–152.
[113] Cornelia S, Mark T. Goodness-of-fit Tests for Parametric Families ofArchimedean Copulas[R]. Münster: University of Muenster, 2004.
[114] Bickel P, Rosenblatt M. On some global meansures of the deviation of densityfunction estimates[J]. Annals of Statistics, 1973, 1:1071–1095.
[115] Joe H. Multivariate models and dependence concepts[M]. London: Chapmanand Hall, 1999.
[116]梁冯珍,钟君,史道济.尾部相关性对投资组合VaR的影响分析[J].系统工程理论与实践, 2007, 27(7):64–68.
[117] Sibuya M. Bivariate extreme statistics.[J]. Annals of the Institute of StatisticalMathematics, 1960(11):195–210.
[118] Coles J, S.G.and Heffernan, Tawn J A. Dependence measures for multivariateextremes[J]. Extremes, 1999, 2:339–365.
[119]史道济,孙炳堃.二元Cauchy分布尾部的相关性[J].天津大学学报, 2000,33(4):432–434.
[120] Mari D D, Kotz s. Correlation and Dependence[M]. London: Imperial CollegePress, 2001.
[121] R Development Core Team. R: A Language and Environment for StatisticalComputing[H]. R Foundation for Statistical Computing, Vienna, Austria, 2006.http://www.R-project.org. ISBN 3-900051-07-0.
[122] Embrechts P, Lindskog F, McNeil A J. Modelling dependence with copulas andapplications to risk management[M]. Amserdam: Elsevier/North-Holland, 2003.
[123] Matsumoto M, Nishimura T. Mersenne Twister: A 623-dimensionally equidistributeduniform pseudo-random number generator[J]. ACM Transactions onModeling and Computer Simulation, 1998, 8:3–30.
[124] Fishburm P C, Wakker P. The invention of the independence condition for preferences[J]. Management Science, 1995, 41:1130–1144.
[125]王春峰. VaR金融市场风险管理[M].天津:天津大学出版社, 2001.
[126] Dowd K, Cairns A, Blake D. Mortality-dependent financial risk measures[J].Insurance Mathematics & Economics, 2006, 38(3):427– 40. http://dx.doi.org/10.1016/j.insmatheco.2005.11.003.
[127] Ren W, Jin-cheng S, Yang F, et al. Combined bidding strategy and model forpower suppliers based on CVaR risk measurement techniques[J]. Automation ofElectric Power Systems, 2005, 29(14):5– 9.
[128] Delbaen F. Coherent risk measures on general probability spaces[M]. Berlin:Springer-Verlag, 2002.
[129] Boda K, Filar J. Time consistent dynamic risk measures[J]. Mathematical Methodsof Operations Research, 2006, 63(1):169– 86. http://dx.doi.org/10.1007/s00186-005-0045-1.
[130] Sakalauskas V, Kriksciuniene D. Short-term investment risk measurement usingVaR and CVaR[J]. Computational Science-ICCS 2006. 6th International Conference.Proceedings, Part IV (Lecture Notes in Computer Science Vol.3994),2006:316– 23.
[131] Cheng S, Liu Y,Wang S. Progress in Risk Measurement[J]. Advanced Modellingand Optimization, 2004, 6:1–20.