Joint value-at-risk and expected shortfall regression for location-scale time series models

References

• Acereda, B., A. Leon, and J. Mora. 2020. Estimating the expected shortfall of cryptocurrencies: An evaluation based on backtesting. Finance Research Letters 33:101181. doi:10.1016/j.frl.2019.04.037.
   Web of Science ®Google Scholar
• Diebold, F. X., and R. S. Mariano. 1995. Comparing predictive accuracy. Journal of Business & Economic Statistics 13 (3):134–44.
   Web of Science ®Google Scholar
• Dimitriadis, T., and S. Bayer. 2019. A joint quantile and expected shortfall regression framework. Electronic Journal of Statistics 13 (1):1823–71.
   Web of Science ®Google Scholar
• Fissler, T., and J. F. Ziegel. 2016. Higher order elicitability and Osband’s principle. The Annals of Statistics 44 (4):1680–707.
   Web of Science ®Google Scholar
• Fissler, T., J. F. Ziegel, and T. Gneiting, 2015. Expected shortfall is jointly elicitable with value at risk-implications for backtesting. arXiv preprint, arXiv:1507.00244.
   Google Scholar
• Francq, C., and J.-M. Zakoïan. 2015. Risk-parameter estimation in volatility models. Journal of Econometrics 184 (1):158–73. doi:10.1016/j.jeconom.2014.06.019.
   Web of Science ®Google Scholar
• Gao, L., W. Ye, and R. Guo. 2022. Jointly forecasting the value-at-risk and expected shortfall of Bitcoin with a regime-switching CAViaR model. Finance Research Letters 48:102826. doi:10.1016/j.frl.2022.102826.
   Web of Science ®Google Scholar
• Gneiting, T. 2011. Making and evaluating point forecasts. Journal of the American Statistical Association 106 (494):746–62. doi:10.1198/jasa.2011.r10138.
   Web of Science ®Google Scholar
• Hansen, B. E. 1994. Autoregressive conditional density estimation. International Economic Review 35 (3):705. doi:10.2307/2527081.
   Web of Science ®Google Scholar
• Jiao, S., and W. Ye. 2023. Expected shortfall regression for censored data. Communications in Mathematics and Statistics. doi:10.1007/s40304-023-00357-3.
   Web of Science ®Google Scholar
• Koenker, R., and Q. Zhao. 1996. Conditional quantile estimation and inference for arch models. Econometric Theory 12 (5):793–813. doi:10.1017/S0266466600007167.
   Web of Science ®Google Scholar
• Le, T. H. 2020. Forecasting value at risk and expected shortfall with mixed data sampling. International Journal of Forecasting 36 (4):1362–79. doi:10.1016/j.ijforecast.2020.01.008.
   Web of Science ®Google Scholar
• Lee, S., and J. Noh. 2013. Quantile regression estimator for GARCH models. Scandinavian Journal of Statistics 40 (1):2–20. doi:10.1111/j.1467-9469.2011.00759.x.
   Web of Science ®Google Scholar
• Mcneil, A. J., R. Frey, and P. Embrechts, 2015. Quantitative risk management: concepts, techniques and tools-revised edition. Princeton, NJ: Princeton University Press.
   Google Scholar
• Meng, X., and J. W. Taylor. 2020. Estimating value-at-risk and expected shortfall using the intraday low and range data. European Journal of Operational Research 280 (1):191–202. doi:10.1016/j.ejor.2019.07.011.
   Web of Science ®Google Scholar
• Merlo, L., L Petrella, and V. Raponi. 2021. Forecasting VaR and ES using a joint quantile regression and its implications in portfolio allocation. Journal of Banking & Finance 133:106248. doi:10.1016/j.jbankfin.2021.106248.
   Web of Science ®Google Scholar
• Nadarajah, S., Bo. Zhang, and S. Chan. 2014. Estimation methods for expected shortfall. Quantitative Finance 14 (2):271–91. doi:10.1080/14697688.2013.816767.
   Web of Science ®Google Scholar
• Noh, J., and S. Lee. 2016. Quantile regression for location-scale time series models with conditional heteroscedasticity. Scandinavian Journal of Statistics 43 (3):700–20. doi:10.1111/sjos.12199.
   Web of Science ®Google Scholar
• Nolde, N., and J. F. Ziegel. 2017. Elicitability and backtesting: Perspectives for banking regulation. The Annals of Applied Statistics 11 (4):1833–74.
   Web of Science ®Google Scholar
• Patton, A. J., J. F. Ziegel, and R. Chen. 2019. Dynamic semiparametric models for expected shortfall (and Value-at-Risk). Journal of Econometrics 211 (2):388–413. doi:10.1016/j.jeconom.2018.10.008.
   Web of Science ®Google Scholar
• Straumann, D., and T. Mikosch. 2006. Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equations approach. The Annals of Statistics 34 (5):2449–95.
   Web of Science ®Google Scholar
• Taylor, J. W. 2020. Forecast combinations for value at risk and expected shortfall. International Journal of Forecasting 36 (2):428–41. doi:10.1016/j.ijforecast.2019.05.014.
   Web of Science ®Google Scholar
• Xiao, Z., and R. Koenker. 2009. Conditional quantile estimation for generalized autoregressive conditional heteroscedasticity models. Journal of the American Statistical Association 104 (488):1696–712. doi:10.1198/jasa.2009.tm09170.
   Web of Science ®Google Scholar