Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-02-12T10:49:17.912Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMAL MODEL AVERAGING FOR JOINT VALUE-AT-RISK AND EXPECTED SHORTFALL REGRESSION

Published online by Cambridge University Press:  12 February 2025

Shoukun Jiao Open the ORCID record for Shoukun Jiao [Opens in a new window] ,
Wenchao Xu Open the ORCID record for Wenchao Xu [Opens in a new window] ,
Wuyi Ye Open the ORCID record for Wuyi Ye [Opens in a new window]  and
Xinyu Zhang
Shoukun Jiao
Affiliation:
University of Science and Technology of China
Wenchao Xu
Affiliation:
Shanghai University of International Business and Economics
Wuyi Ye*
Affiliation:
University of Science and Technology of China
Xinyu Zhang
Affiliation:
University of Science and Technology of China and Chinese Academy of Sciences
*
Address correspondence to Wuyi Ye, School of Management, University of Science and Technology of China, Hefei, China; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

Since the implementation of the Basel III Accord, expected shortfall (ES) has gained increasing attention from regulators as a complement to value-at-risk (VaR). The problem of elicitability for ES makes jointly modeling VaR and ES a popular method to study ES. In this article, we develop model averaging for joint VaR and ES regression models that selects the two weight vectors by minimizing a jackknife criterion. We show the large sample properties of the estimators under potential model misspecification with increasing dimension of parameters and the asymptotic optimality of the selected weights in the sense of minimizing the out-of-sample excess final prediction error. Simulation studies and three empirical analyses reveal good finite sample performance.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 34
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The authors would like to thank the Co-Editor, Viktor Todorov, and three anonymous referees for their guidance and insightful comments which substantially improved the article. S.J. and W.Y. thank research support by the National Natural Science Foundation of China (Grant No. 72371230) and the Anhui Provincial Natural Science Foundation (Grant No. 2208085J41). W.X. thanks research support by the National Natural Science Foundation of China (Grant No. 12101591). X.Z. thanks research support by the National Natural Science Foundation of China (Grant Nos. 71925007, 72091212, and 71988101).

S.J. and W.X. have contributed equally to this work and should be considered co-first authors.

References

REFERENCES

Ando, T., & Li, K.-C. (2014). A model-averaging approach for high-dimensional regression. Journal of the American Statistical Association , 109(505), 254–265.CrossRefGoogle Scholar
Bai, Y., Jiang, R., & Zhang, M. (2022). Optimal model averaging estimator for expectile regressions. Journal of Statistical Planning and Inference , 217, 204–223.CrossRefGoogle Scholar
Buckland, S. T., Burnham, K. P., & Augustin, N. H. (1997). Model selection: An integral part of inference. Biometrics , 53(2), 603–618.CrossRefGoogle Scholar
Clyde, M., & George, E. I. (2004). Model uncertainty. Statistical Science , 19(1), 81–94.CrossRefGoogle Scholar
Dimitriadis, T., & Bayer, S. (2019). A joint quantile and expected shortfall regression framework. Electronic Journal of Statistics , 13(1), 1823–1871.CrossRefGoogle Scholar
Elliott, G., Gargano, A., & Timmermann, A. (2013). Complete subset regressions. Journal of Econometrics , 177(2), 357–373.CrossRefGoogle Scholar
Fissler, T., & Ziegel, J. F. (2016). Higher order elicitability and Osband’s principle. The Annals of Statistics , 44(4), 1680–1707.CrossRefGoogle Scholar
Gneiting, T. (2011). Making and evaluating point forecasts. Journal of the American Statistical Association , 106(494), 746–762.CrossRefGoogle Scholar
Hansen, B. E. (1994). Autoregressive conditional density estimation. International Economic Review , 35(3), 705–730.CrossRefGoogle Scholar
Hansen, B. E. (2007). Least squares model averaging. Econometrica , 75(4), 1175–1189.CrossRefGoogle Scholar
Hansen, B. E., & Racine, J. S. (2012). Jackknife model averaging. Journal of Econometrics , 167(1), 38–46.CrossRefGoogle Scholar
Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999). Bayesian model averaging: A tutorial. Statistical Science , 14(4), 382–417.Google Scholar
Koenker, R., & Bassett, G. (1982). Robust tests for heteroscedasticity based on regression quantiles. Econometrica , 50(1), 43–61.CrossRefGoogle Scholar
Li, X., Zou, G., Zhang, X., & Zhao, S. (2021). Least squares model averaging based on generalized cross validation. Acta Mathematicae Applicatae Sinica, English Series , 37(3), 495–509.CrossRefGoogle Scholar
Liu, C.-A., & Kuo, B.-S. (2016). Model averaging in predictive regressions. The Econometrics Journal , 19(2), 203–231.CrossRefGoogle Scholar
Lu, X., & Su, L. (2015). Jackknife model averaging for quantile regressions. Journal of Econometrics , 188(1), 40–58.CrossRefGoogle Scholar
Magnus, J. R., Powell, O., & Prüfer, P. (2010). A comparison of two model averaging techniques with an application to growth empirics. Journal of Econometrics , 154(2), 139–153.CrossRefGoogle Scholar
Newey, W. K., & McFadden, D. (1994). Large sample estimation and hypothesis testing. In Engle, R. and Mcfadden, D., editors. Handbook of Econometrics , 4, 2111–2245.CrossRefGoogle Scholar
Patton, A. J., Ziegel, J. F., & Chen, R. (2019). Dynamic semiparametric models for expected shortfall (and value-at-risk). Journal of Econometrics , 211(2), 388–413.CrossRefGoogle Scholar
Peng, J., & Yang, Y. (2022). On improvability of model selection by model averaging. Journal of Econometrics , 229(2), 246–262.CrossRefGoogle Scholar
Sun, Y., Hong, Y., Lee, T.-H., Wang, S., & Zhang, X. (2021). Time-varying model averaging. Journal of Econometrics , 222(2), 974–992.CrossRefGoogle Scholar
Taylor, J. W. (2019). Forecasting value at risk and expected shortfall using a semiparametric approach based on the asymmetric Laplace distribution. Journal of Business & Economic Statistics , 37(1), 121–133.CrossRefGoogle Scholar
Taylor, J. W. (2020). Forecast combinations for value at risk and expected shortfall. International Journal of Forecasting , 36(2), 428–441.CrossRefGoogle Scholar
Tu, Y., & Wang, S. (2020). Jackknife model averaging for expectile regressions in increasing dimension. Economics Letters , 197, 109607.CrossRefGoogle Scholar
Van der Vaart, A. W., & Wellner, J. A. (1996). Weak convergence and empirical processes: With applications to statistics . Springer.CrossRefGoogle Scholar
Wang, M., Zhang, X., Wan, A. T., You, K., & Zou, G. (2023). Jackknife model averaging for high-dimensional quantile regression. Biometrics , 79(1), 178–189.CrossRefGoogle ScholarPubMed
Weber, S. (2006). Distribution-invariant risk measures, information, and dynamic consistency. Mathematical Finance , 16(2), 419–441.CrossRefGoogle Scholar
Weiss, A. A. (1991). Estimating nonlinear dynamic models using least absolute error estimation. Econometric Theory , 7(1), 46–68.CrossRefGoogle Scholar
Welch, I., & Goyal, A. (2008). A comprehensive look at the empirical performance of equity premium prediction. The Review of Financial Studies , 21(4), 1455–1508.CrossRefGoogle Scholar
Wooldridge, J. M. (2015). Introductory econometrics: A modern approach . Cengage Learning.Google Scholar
Yuan, Z., & Yang, Y. (2005). Combining linear regression models: When and how? Journal of the American Statistical Association , 100(472), 1202–1214.CrossRefGoogle Scholar
Zhang, X., Wan, A. T., & Zou, G. (2013). Model averaging by jackknife criterion in models with dependent data. Journal of Econometrics , 174(2), 82–94.CrossRefGoogle Scholar
Supplementary material: File

Jiao et al. supplementary material

Jiao et al. supplementary material
Download Jiao et al. supplementary material(File)
File 573.7 KB