Value-at-risk forecasting based on Gaussian mixture ARMA–GARCH model

References

• Jorion , P. 2006 . Value At Risk: The New Benchmark for Managing Financial Risk , Boston : McGraw-Hill .
   Google Scholar
• Venkataraman , S. 1997 . Value at risk for a mixture of normal distributions: The use of quasi-Bayesian estimation techniques . Econ. Perspect. , 21 : 2 – 13 .
   Google Scholar
• Bollerslev , T. 1986 . Generalized autoregressive conditional heteroskedasticity . J. Econ. , 31 : 307 – 327 .
   Web of Science ®Google Scholar
• Brooks , C. and Persand , G. 2003 . The effect of asymmetries on stock index return value-at-risk estimates . J. Risk Finance , 4 : 29 – 42 .
   Google Scholar
• Mittnik , S. and Paolella , M. S. 2000 . Conditional density and value-at-risk prediction of Asian currency exchange rates . J. Emp. Finance , 7 : 389 – 416 .
   Google Scholar
• Haas , M. , Mittnik , S. and Paolella , M. S. 2004 . Mixed normal conditional heteroskedasticity . J. Financ. Econ. , 2 : 211 – 250 .
   Google Scholar
• Hartz , C. , Mittnik , S. and Paolella , M. 2006 . Accurate value-at-risk forecasting based on the normal-GARCH model . Comput. Stat. Data Anal. , 50 : 3032 – 3052 .
   Google Scholar
• McLachlan , G. and Peel , D. 2000 . Finite Mixture Models , New York : Wiley .
   Google Scholar
• Ausín , M. C. and Galeano , P. 2007 . Bayesian estimation of the Gaussian mixture GARCH model . Comput. Statist. Data Anal. , 51 : 2636 – 2652 .
   Web of Science ®Google Scholar
• Demsper , A. P. , Laird , N. M. and Rubin , D. B. 1977 . Large maximum-likelihood from incomplete data via the EM algorithm . J. R. Stat. Soc. Ser. B , 39 : 1 – 38 .
   Google Scholar
• Redner , R. and Walker , H. F. 1984 . Mixture densities, maximum likelihood and the EM algorithm . SIAM Rev. , 26 : 195 – 239 .
   Web of Science ®Google Scholar
• Wong , C. S. and Li , W. K. 2001 . On a mixture autoregressive conditional heteroscedastic model . J. Am. Stat. Assoc. , 96 : 982 – 995 .
   Web of Science ®Google Scholar
• Francq , C. and Zakoïan , J. 2004 . Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes . Bernoulli , 10 : 605 – 637 .
   Web of Science ®Google Scholar
• Woodward , W. A. , Parr , W. C. , Schucany , W. R. and Lindsay , H. 1984 . A comparison of minimum distance and maximum likelihood estimation of a mixture proportion . J. Am. Stat. Assoc. , 79 : 590 – 598 .
   Web of Science ®Google Scholar
• Lee , T. and Lee , S. 2009 . Normal mixture quasi-maximum likelihood estimator for GARCH models . Scand. J. Statist. , 36 : 157 – 170 .
   Web of Science ®Google Scholar
• Ding , Z. , Granger , C. W. and Engle , R. F. 1993 . A long memory property of stock market returns and a new model . J. Emp. Finance , 1 : 83 – 106 .
   Google Scholar
• Paolella , M. S. 2001 . Testing the stable Paretian assumption . Math. Comput. Model. , 34 : 1095 – 1112 .
   Web of Science ®Google Scholar
• Giot , P. and Laurent , S. 2004 . Modelling daily value-at-risk using realized volatility and arch type models . J. Emp. Finance , 11 : 379 – 398 .
   Google Scholar
• Kupiec , P. H. 1995 . Techniques for verifying the accuracy of risk measurement models . J. Derivatives , 3 : 73 – 84 .
   Google Scholar
• Christoffersen , P. F. 1998 . Evaluating interval forecasts . Int. Econ. Rev. , 39 : 841 – 861 .
   Web of Science ®Google Scholar
• Hwang , S. Y. and Basawa , I. V. 2004 . Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes . Statist. Probab. Lett. , 68 : 209 – 220 .
   Web of Science ®Google Scholar
• Leroux , B. G. 1992 . Consistent estimation of a mixing distribution . Ann. Statist. , 20 : 1350 – 1360 .
   Web of Science ®Google Scholar
• Redner , R. 1981 . Note on the consistency of the maximum likelihood estimate for nonidentifiable distribution . Ann. Stat. , 9 : 225 – 228 .
   Web of Science ®Google Scholar
• Bougerol , P. and Picard , N. 1992 . Stationary of GARCH processes and of some nonnegative time series . J. Econ. , 52 : 115 – 127 .
   Web of Science ®Google Scholar
• Ling , S. and McAleer , M. 2002 . Stationarity and the existence of moments of a family of GARCH processes . J. Econ. , 106 : 109 – 117 .
   Web of Science ®Google Scholar