References
- Angelidis T, Benos A, Degiannakis S. The use of GARCH models in VaR estimation. Stat Methodol. 2004;1(1):105–128. doi: 10.1016/j.stamet.2004.08.004
- Bali TG, Theodossiou P. A conditional-SGT-VaR approach with alternative GARCH models. Ann Oper Res. 2007;151(1):241–267. doi: 10.1007/s10479-006-0118-4
- Braione M, Scholtes NK. Forecasting value-at-risk under different distributional assumptions. Econometrics. 2016;4(3):1–27.
- Harmantzis FC, Miao L, Chien Y. Empirical study of value-at-risk and expected shortfall models with heavy tails. J Risk Finance. 2006;7(2):117–135. doi: 10.1108/15265940610648571
- Hung JC, Lee MC, Liu HC. Estimation of value-at-risk for energy commodities via fat-tailed GARCH models. Energy Econ. 2008;30(3):1173–1191. doi: 10.1016/j.eneco.2007.11.004
- Lee MC, Su JB, Liu HC. Value-at-risk in US stock indices with skewed generalized error distribution. Appl Financ Econ Lett. 2008;4(6):425–431. doi: 10.1080/17446540701765274
- Lee CF, Su JB. Alternative statistical distributions for estimating value-at-risk: theory and evidence. Rev Quant Financ Account. 2012;39(3):309–331. doi: 10.1007/s11156-011-0256-x
- Nelson D. Conditional heteroscedasticity in asset returns: a new approach. Econometrica. 1991;59:347–370. doi: 10.2307/2938260
- Venkataraman S. Value at risk for a mixture of normal distributions: the use of quasi-Bayesian estimation techniques. Econ Perspect Fed Reserve Bank Chicago. 1997;21:2–13.
- Zangari P. An improved methodology for measuring VaR. Risk Metrics Monit. 1996;2(1):7–25.
- Guermat C, Harris RD. Forecasting value at risk allowing for time variation in the variance and kurtosis of portfolio returns. Int J Forecast. 2002;18(3):409–419. doi: 10.1016/S0169-2070(01)00122-4
- Giot P, Laurent S. Market risk in commodity markets: a VaR approach. Energy Econ. 2003a;25(5):435–457. doi: 10.1016/S0140-9883(03)00052-5
- Giot P, Laurent S. Value-at-risk for long and short trading positions. J Appl Econ. 2003b;18(6):641–663. doi: 10.1002/jae.710
- Brooks C, Persand G. Model choice and value-at-risk performance. Financ Anal J. 2002;58(5):87–97. doi: 10.2469/faj.v58.n5.2471
- Lyu Y, Wang P, Wei Y, et al. Forecasting the VaR of crude oil market: do alternative distributions help?. Energy Econ. 2017;66:523–534. doi: 10.1016/j.eneco.2017.06.015
- Altun E, Tatlidil H, Ozel G, et al. A new generalization of skew-T distribution with volatility models. J Stat Comput Simul. 2018;88(7):1252–1272. doi: 10.1080/00949655.2018.1427240
- Robertson JS. Gudermann and the simple pendulum. Coll Math J. 1997;28(4):271–276. doi: 10.1080/07468342.1997.11973874
- Fogiel M. Handbook of mathematical, scientific, and engineering formulas, tables, functions, graphs, transforms. Piscataway (NJ): Research & Education Association; 1984.
- Elal-Olivero D. Alpha-skew-normal distribution. Proyecciones (Antofagasta). 2010;29(3):224–240. doi: 10.4067/S0716-09172010000300006
- Bollerslev T. Generalized autoregressive conditional heteroskedasticity. J Econom. 1986;31(3):307–327. doi: 10.1016/0304-4076(86)90063-1
- Engle RF. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econ: J Econ Soc. 1982;50(4):987–1007. doi: 10.2307/1912773
- Azzalini A. A class of distributions which includes the normal ones. Scand J Stat. 1985;12:171–178.
- Bollerslev T. A conditionally heteroskedastic time series model for speculative prices and rates of return. Rev Econ Stat. 1987;69:542–547. doi: 10.2307/1925546
- Christoffersen PF. Evaluating interval forecasts. Int Econ Rev (Philadelphia). 1998;39:841–862. doi: 10.2307/2527341
- Kupiec PH. Techniques for verifying the accuracy of risk measurement models. J Derivatives. 1995;3(2):73–84. doi: 10.3905/jod.1995.407942
- Sarma M, Thomas S, Shah A. Selection of value-at-risk models. J Forecast. 2003;22(4):337–358. doi: 10.1002/for.868
- D'Agostino RB. Transformation to normality of the null distribution of g1. Biometrika. 1970;57:679–681.
- Anscombe FJ, Glynn WJ. Distribution of the kurtosis statistic b2 for normal samples. Biometrika. 1983;70(1):227–234.