本篇論文主要是依據Patton(2006)與Huang et al.(2009)的研究，將copula-GARCH方法應用至美國的不動產投資信託市場中，以探討模型是否能有效改善對於REITs資產組合風險值的預測能力及績效。我們使用美國國家不動產投資信託協會之REITs指數(FTSE NAREIT US Real Estate Index - All REITs)與S&P 500股價指數組成投資組合，並使用GARCH模型來描述指數報酬率序列相關的特性，最後以5個常數copula與2類動態copula共7種copula函數分別搭配個別資產報酬率服從常態分配與Student-t分配之GARCH(1,1)模型共組合出14種copula-GARCH模型來估計兩資產報酬率的聯合分配，進而推導出投資組合的一日風險值，樣本期間涵蓋金融風暴發生前後共2800個觀察值，並與一般風險值估計方法進行回溯測試結果的比較。Copula-GARCH模型同時考慮了個別指數報酬率序列相關的性質與不同金融資產間非線性相關的部分，並且修正了傳統風險值模型之常態性假設所無法捕捉到的資產分配現象，本研究的實證結果顯示，邊際分配服從GARCH-t之time-varying SJC copula不論在市場狀況好壞時相對於傳統風險值模型確實能夠更加精確的掌握REITs資產組合的風險。

Akaike, H., 1974, A new look at the statistical model identification, Automatic Control, IEEE Transactions on, 19(6), 716-723

Clayton, D. G., 1978, A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika, 65(1), 141-151

Clayton, J., and G. MacKinnon, 2001, The Time-Varying Nature of the Link between REIT, Real Estate and Financial Asset Returns, Journal of Real Estate Portfolio Management, 7(1), 43-54

Clayton, J., and G. MacKinnon, 2003, The Relative Importance of Stock, Bond and Real Estate Factors in Explaining REIT Returns, Journal of Real Estate Finance and Economics, 27(1), 39-60

Cotter, J., and S. Stevenson, 2007, Uncovering Volatility Dynamics in Daily REIT Returns, Journal of Real Estate Portfolio Management, 13(2), 119-128

Engle, R. F., 1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica: Journal of the Econometric Society, 987-1007

Fei, P., L. Ding, and Y. Deng, 2010, Correlation and Volatility Dynamics in REIT Returns: Performance and Portfolio Considerations, The Journal of Portfolio Management, 36(2), 113-125

Frank, M. J., 1979, On the simultaneous associativity of F(x,y) and x+y-F(x,y), Aequationes Mathematicae, 19(1), 194-226
 
Ghosh, C., M. Miles, and C. F. Sirmans, 1996, Are REITs Stocks?, Real Estate Finance, 13, 46-53

Gumbel, E. J., 1960, Bivariate Exponential Distributions, Journal of the American Statistical Association, 55(292), 698-707

Han, J., and Y. Liang, 1995, The Historical Performance of Real Estate Investment Trust, The Journal of Real Estate Research, 10(3), 235-262

Huang, J. J., K. J. Lee, H. Liang, and W. F. Lin, 2009, Estimating value at risk of portfolio by conditional copula-GARCH method, Journal of Insurance: Mathematics and Economics, 45(3), 315-324

Huang, J. Z., and Z. K. Zhong, 2013, Time variation in diversification benefits of commodity, REITs, and TIPS, The Journal of Real Estate Finance and Economics, 46(1), 152-192

Hull, J., 2012, Options, Futures and Other Derivatives, 8/e, Pearson Education India

Joe, H.,1997, Multivariate models and multivariate dependence concepts, Vol. 73, CRC Press

Joe, H.,2005, Asymptotic efficiency of the two-stage estimation method for copula-based models, Journal of Multivariate Analysis, 94(2), 401-419

Jondeau, E., and M. Rockinger, 2006, The copula-garch model of conditional dependencies: An international stock market application Journal of international money and finance, 25(5), 827-853

JP Morgan, 1996, Riskmetrics: technical document, Morgan Guaranty Trust Company of New York

Kang, Z., and D. Choi, 2011, How is the Equity REIT Sector Related to Other Major Equity Sectors in the Presence of Abnormal Returns and Volatilities? A Tail Effect Study, Journal of Real Estate Portfolio Management, 17(2), 89-111

Kupiec, P. H., 1995, Techniques for verifying the accuracy of risk measurement models, THE J. OF DERIVATIVES, 3(2)

Liang, Y., and W. McIntosh, 1998, REIT Style and Performance, Journal of Real Estate Portfolio Management, 4(1), 69-78

Lu, C. L., S. C. Wu, and L. C. Ho, 2009, Applying VaR to REITs: A comparison of alternative methods, Review of Financial Economics, 18(2), 97-102

Mueller, G. R., K. R. Pauley, and W. K. Morrill, 1994, Should REITs Be Included in A Mixed-Asset Portfolio?, Real Estate Finance, 11(1), 23-28

Nelsen, R. B., 2006, An Introduction to Copulas, Springer

Palaro, H. P., and L. K. Hotta, 2006, Using Conditional Copula to Estimate Value at Risk, Journal of Data Science, 4(1), 93-115

Patton, A. J., 2004, On the out-of-sample importance of skewness and asymmetric dependence for asset allocation, Journal of Financial Econometrics, 2(1), 130-168

Patton, A. J., 2006, Modelling asymmetric exchange rate dependence, International economic review, 47(2) 527-556

Rong, N., and S. Trück, 2010, Returns of REITS and stock markets: Measuring dependence and risk, Journal of Property Investment & Finance, 28(1), 34-57

Sklar, A., 1959, Fonctions de répartition à n dimensions et leurs marges, Publications de l’Institut Statistuque de l’Universite de Paris 8, 229-231

Simon, S., and W. L. Ng, 2009, The Effect of the Real Estate Downturn on the Link between REITs and the Stock Market, Journal of Real Estate Portfolio Management, 15(3), 211-219

Yan, J., 2007, Enjoy the Joy of Copulas: With a Package copula, Journal of Statistical Software, 21(4), 1-21

Zeiring, B., B. Winograd, and W. McIntosh, 1997, The Evolution of Public and Private Market Investing in the New Real Estate Capital Markets, Real Estate Finance, 14, 21-28

Zhou, J., and R. I. Anderson, 2012, Extreme risk measures for international REIT markets, The Journal of Real Estate Finance and Economics, 45(1), 152-170