IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1908.04569.html
   My bibliography  Save this paper

Forecast Encompassing Tests for the Expected Shortfall

Author

Listed:
  • Timo Dimitriadis
  • Julie Schnaitmann

Abstract

We introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). The ES currently receives much attention through its introduction into the Basel III Accords, which stipulate its use as the primary market risk measure for the international banking regulation. We utilize joint loss functions for the pair ES and Value at Risk to set up three ES encompassing test variants. The tests are built on misspecification robust asymptotic theory and we investigate the finite sample properties of the tests in an extensive simulation study. We use the encompassing tests to illustrate the potential of forecast combination methods for different financial assets.

Suggested Citation

  • Timo Dimitriadis & Julie Schnaitmann, 2019. "Forecast Encompassing Tests for the Expected Shortfall," Papers 1908.04569, arXiv.org, revised Aug 2020.
    • Handle: RePEc:arx:papers:1908.04569
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1908.04569
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
    2. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    3. Otávio Bartalotti, 2013. "GMM Efficiency and IPW Estimation for Nonsmooth Functions," Working Papers 1301, Tulane University, Department of Economics.
    4. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    5. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    7. Michael P. Clements & David I. Harvey, 2009. "Forecast Combination and Encompassing," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 4, pages 169-198, Palgrave Macmillan.
    8. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    9. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024.
    10. Michael P. Clements & David I. Harvey, 2010. "Forecast encompassing tests and probability forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(6), pages 1028-1062.
    11. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
    12. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    13. Diebold, Francis X., 1989. "Forecast combination and encompassing: Reconciling two divergent literatures," International Journal of Forecasting, Elsevier, vol. 5(4), pages 589-592.
    14. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    15. Graham Elliott & Allan Timmermann & Ivana Komunjer, 2005. "Estimation and Testing of Forecast Rationality under Flexible Loss," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(4), pages 1107-1125.
    16. Yock Y. Chong & David F. Hendry, 1986. "Econometric Evaluation of Linear Macro-Economic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 671-690.
    17. Sander Barendse, 2017. "Interquantile Expectation Regression," Tinbergen Institute Discussion Papers 17-034/III, Tinbergen Institute.
    18. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    19. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    20. Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
    21. Halbleib, Roxana & Pohlmeier, Winfried, 2012. "Improving the value at risk forecasts: Theory and evidence from the financial crisis," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1212-1228.
    22. David Harvey & Paul Newbold, 2000. "Tests for multiple forecast encompassing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 471-482.
    23. Stefan Weber, 2006. "Distribution‐Invariant Risk Measures, Information, And Dynamic Consistency," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 419-441, April.
    24. Patton, Andrew J. & Timmermann, Allan, 2007. "Testing Forecast Optimality Under Unknown Loss," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1172-1184, December.
    25. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    26. C. Heinrich, 2014. "The mode functional is not elicitable," Biometrika, Biometrika Trust, vol. 101(1), pages 245-251.
    27. Hendry, David F. & Richard, Jean-Francois, 1982. "On the formulation of empirical models in dynamic econometrics," Journal of Econometrics, Elsevier, vol. 20(1), pages 3-33, October.
    28. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    29. Tobias Fissler & Johanna F. Ziegel, 2019. "Evaluating Range Value at Risk Forecasts," Papers 1902.04489, arXiv.org, revised Nov 2020.
    30. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    31. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-678, May.
    32. James W. Taylor, 2019. "Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 121-133, January.
    33. Bayer, Sebastian, 2018. "Combining Value-at-Risk forecasts using penalized quantile regressions," Econometrics and Statistics, Elsevier, vol. 8(C), pages 56-77.
    34. Hajo Holzmann & Matthias Eulert, 2014. "The role of the information set for forecasting - with applications to risk management," Papers 1404.7653, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dimitriadis, Timo & Liu, Xiaochun & Schnaitmann, Julie, 2020. "Encompassing tests for value at risk and expected shortfall multi-step forecasts based on inference on the boundary," Hohenheim Discussion Papers in Business, Economics and Social Sciences 11-2020, University of Hohenheim, Faculty of Business, Economics and Social Sciences.
    2. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146, arXiv.org, revised Sep 2022.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dimitriadis, Timo & Schnaitmann, Julie, 2021. "Forecast encompassing tests for the expected shortfall," International Journal of Forecasting, Elsevier, vol. 37(2), pages 604-621.
    2. Timo Dimitriadis & Xiaochun Liu & Julie Schnaitmann, 2020. "Encompassing Tests for Value at Risk and Expected Shortfall Multi-Step Forecasts based on Inference on the Boundary," Papers 2009.07341, arXiv.org.
    3. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    4. David Happersberger & Harald Lohre & Ingmar Nolte, 2020. "Estimating portfolio risk for tail risk protection strategies," European Financial Management, European Financial Management Association, vol. 26(4), pages 1107-1146, September.
    5. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146, arXiv.org, revised Sep 2022.
    6. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    7. Şener, Emrah & Baronyan, Sayad & Ali Mengütürk, Levent, 2012. "Ranking the predictive performances of value-at-risk estimation methods," International Journal of Forecasting, Elsevier, vol. 28(4), pages 849-873.
    8. Alessandra Amendola & Vincenzo Candila & Antonio Naimoli & Giuseppe Storti, 2024. "Adaptive combinations of tail-risk forecasts," Papers 2406.06235, arXiv.org.
    9. Patrick Schmidt & Matthias Katzfuss & Tilmann Gneiting, 2021. "Interpretation of point forecasts with unknown directive," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(6), pages 728-743, September.
    10. Sebastian Bayer & Timo Dimitriadis, 2022. "Regression-Based Expected Shortfall Backtesting [Backtesting Expected Shortfall]," Journal of Financial Econometrics, Oxford University Press, vol. 20(3), pages 437-471.
    11. Federico Gatta & Fabrizio Lillo & Piero Mazzarisi, 2024. "CAESar: Conditional Autoregressive Expected Shortfall," Papers 2407.06619, arXiv.org.
    12. Yen, Yu-Min & Yen, Tso-Jung, 2021. "Testing forecast accuracy of expectiles and quantiles with the extremal consistent loss functions," International Journal of Forecasting, Elsevier, vol. 37(2), pages 733-758.
    13. Carlos Trucíos & James W. Taylor, 2023. "A comparison of methods for forecasting value at risk and expected shortfall of cryptocurrencies," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(4), pages 989-1007, July.
    14. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    15. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    16. Komunjer, Ivana, 2013. "Quantile Prediction," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 961-994, Elsevier.
    17. Tobias Fissler & Yannick Hoga, 2021. "Backtesting Systemic Risk Forecasts using Multi-Objective Elicitability," Papers 2104.10673, arXiv.org, revised Feb 2022.
    18. Mauro Bernardi & Leopoldo Catania, 2016. "Comparison of Value-at-Risk models using the MCS approach," Computational Statistics, Springer, vol. 31(2), pages 579-608, June.
    19. Gerlach, Richard & Wang, Chao, 2020. "Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures," International Journal of Forecasting, Elsevier, vol. 36(2), pages 489-506.
    20. Avdulaj, Krenar & Barunik, Jozef, 2015. "Are benefits from oil–stocks diversification gone? New evidence from a dynamic copula and high frequency data," Energy Economics, Elsevier, vol. 51(C), pages 31-44.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1908.04569. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.