E-backtesting

References

• Acerbi C, Székely B (2014) Backtesting Expected Shortfall. Risk Magazine 27(11):76–81.Google Scholar
• Acerbi C, Székely B (2017) General properties of backtestable statistics. Preprint, submitted January 24, https://dx.doi.org/10.2139/ssrn.2905109.Google Scholar
• Agrawal S, Koolen W, Juneja S (2021) Optimal best-arm identification methods for tail-risk measures. Adv. Neural Inform. Processing Systems 34:25578–25590.Google Scholar
• Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
• Basak S, Shapiro A (2001) Value-at-risk-based risk management: Optimal policies and asset prices. Rev. Financial Stud. 14(2):371–405.Crossref, Google Scholar
• Bayer S, Dimitriadis T (2022) Regression-based Expected Shortfall backtesting. J. Financial Econometrics 20(3):437–471.Crossref, Google Scholar
• BCBS (2013) Consultative document: Fundamental review of the trading book (October 2013). Bank for International Settlements, https://www.bis.org/publ/bcbs219.pdf.Google Scholar
• BCBS (2016) Minimum capital requirements for market risk (February 2016). Bank for International Settlements, https://www.bis.org/bcbs/publ/d352.pdf.Google Scholar
• BCBS (2019) Minimum capital requirements for market risk (January 2019). Bank for International Settlements, https://www.bis.org/bcbs/publ/d457.pdf.Google Scholar
• Berkes I, Gombay E, Horváth L, Kokoszka P (2004) Sequential change-point detection in GARCH (p, q) models. Econom. Theory 20(6):1140–1167.Crossref, Google Scholar
• Berkowitz J, Christoffersen P, Pelletier D (2011) Evaluating Value-at-Risk models with desk-level data. Management Sci. 57(12):2213–2227.Link, Google Scholar
• Casgrain P, Larsson M, Ziegel J (2024) Sequential testing for elicitable functionals via supermartingales. Bernoulli 30(2):1347–1374.Crossref, Google Scholar
• Christoffersen PF (1998) Evaluating interval forecasts. Internat. Econom. Rev. 39(4):841–862.Crossref, Google Scholar
• Christoffersen PF (2011) Elements of Financial Risk Management, 2nd ed. (Academic Press, New York).Google Scholar
• Chu JCS, Stinchcombe M, White H (1996) Monitoring structural change. Econometrica 64(5):1045–1065.Crossref, Google Scholar
• Clark TE, McCracken MW (2001) Tests of equal forecast accuracy and encompassing for nested models. J. Econom. 105(1):85–110.Crossref, Google Scholar
• Darling DA, Robbins H (1967) Confidence sequences for mean, variance, and median. Proc. Natl. Acad. Sci. USA 58(1):66–68.Crossref, Google Scholar
• de la Peña VH, Klass MJ, Lai TL (2004) Self-normalized processes: Exponential inequalities, moment bounds and iterated logarithm laws. Ann. Probab. 32(3):1902–1933.Crossref, Google Scholar
• de la Peña VH, Lai TL, Shao QM (2009) Self-Normalized Processes: Limit Theory and Statistical Applications. Probability and Its Applications, 1st ed. (Springer, Berlin).Google Scholar
• DeMiguel V, Garlappi L, Uppal R (2009) Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Rev. Financial Stud. 22(5):1915–1953.Crossref, Google Scholar
• Diebold FX, Mariano RS (1995) Comparing predictive accuracy. J. Bus. Econom. Statist. 13(3):253–263.Crossref, Google Scholar
• Du Z, Escanciano JC (2017) Backtesting Expected Shortfall: Accounting for tail risk. Management Sci. 63(4):940–958.Link, Google Scholar
• Embrechts P, Mao T, Wang Q, Wang R (2021) Bayes risk, elicitability, and the Expected Shortfall. Math. Finance 31(4):1190–1217.Crossref, Google Scholar
• Engle RF, Manganelli S (2004) Caviar: Conditional autoregressive Value at Risk by regression quantiles. J. Bus. Econom. Statist. 22(4):367–381.Crossref, Google Scholar
• Escanciano JC, Olmo J (2010) Backtesting parametric value-at-risk with estimation risk. J. Bus. Econom. Statist. 28(1):36–51.Crossref, Google Scholar
• Fissler T, Holzmann H (2022) Measurability of functionals and of ideal point forecasts. Electronic J. Statist. 16(2):5019–5034.Crossref, Google Scholar
• Fissler T, Ziegel JF (2016) Higher order elicitability and Osband’s principle. Ann. Statist. 44(4):1680–1707.Crossref, Google Scholar
• Föllmer H, Schied A (2016) Stochastic Finance, 4th ed. (De Gruyter, Berlin).Crossref, Google Scholar
• Frongillo R, Kash IA (2021) Elicitation complexity of statistical properties. Biometrika 108(4):857–879.Crossref, Google Scholar
• Giacomini R, White H (2006) Tests of conditional predictive ability. Econometrica 74(6):1545–1578.Crossref, Google Scholar
• Gneiting T (2011) Making and evaluating point forecasts. J. Amer. Statist. Assoc. 106(494):746–762.Crossref, Google Scholar
• Grünwald P, de Heide R, Koolen WM (2024) Safe testing. J. Royal Statist. Soc. Ser. B 86(5):1091–1128.Crossref, Google Scholar
• Henzi A, Ziegel JF (2022) Valid sequential inference on probability forecast performance. Biometrika 109(3):647–663.Crossref, Google Scholar
• Hoga Y, Demetrescu M (2023) Monitoring Value-at-Risk and Expected Shortfall forecasts. Management Sci. 69(5):2954–2971.Link, Google Scholar
• Jang K, Jun KS, Kuzborskij I, Orabona F (2023) Tighter PAC-Bayes bounds through coin-betting. Proc. Thirty-Sixth Conf. Learn. Theory, Proceedings of Machine Learning Research, vol. 195 (PMLR, New York), 2240–2264.Google Scholar
• Kelly JL (1956) A new interpretation of information rate. Bell System Tech. J. 35(4):917–926.Crossref, Google Scholar
• Kupiec P (1995) Techniques for verifying the accuracy of risk measurement models. J. Derivatives 3(2):73–84.Crossref, Google Scholar
• McNeil AJ, Frey R (2000) Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach. J. Empirical Finance 7(3–4):271–300.Crossref, Google Scholar
• McNeil AJ, Frey R, Embrechts P (2015) Quantitative Risk Management: Concepts, Techniques and Tools, rev. ed. (Princeton University Press, Princeton, NJ).Google Scholar
• Mencía J, Sentana E (2009) Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation. J. Econometrics 153(2):105–121.Crossref, Google Scholar
• Moldenhauer F, Pitera M (2019) Backtesting expected shortfall: A simple recipe? J. Risk 22(1):17–42.Crossref, Google Scholar
• Nolde N, Ziegel JF (2017) Elicitability and backtesting: Perspectives for banking regulation (with discussion). Ann. Appl. Statist. 11(4):1833–1874.Google Scholar
• Ramdas A, Wang R (2024) Hypothesis testing with e-values. Preprint, submitted October 31, https://arxiv.org/abs/2410.23614.Google Scholar
• Ramdas A, Grünwald P, Vovk V, Shafer G (2023) Game-theoretic statistics and safe anytime-valid inference. Statist. Sci. 38(4):576–601.Crossref, Google Scholar
• Ren Z, Barber RF (2024) Derandomized knockoffs: Leveraging e-values for false discovery rate control. J. Royal Statist. Soc. Ser. B 86(1):122–154.Crossref, Google Scholar
• Rockafellar RT, Uryasev S (2002) Conditional Value-at-Risk for general loss distributions. J. Banking Finance 26(7):1443–1471.Crossref, Google Scholar
• Schmeidler D (1989) Subjective probability and expected utility without additivity. Econometrica 57(3):571–587.Crossref, Google Scholar
• Shafer G (2021) The language of betting as a strategy for statistical and scientific communication. J. Royal Statist. Soc. Ser. A 184(2):407–431.Crossref, Google Scholar
• Shafer G, Vovk V (2019) Game-Theoretic Foundations for Probability and Finance (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
• Shafer G, Shen A, Vereshchagin N, Vovk V (2011) Test martingales, Bayes factors and p-values. Statist. Sci. 26(1):84–101.Crossref, Google Scholar
• Su Q, Qin Z, Peng L, Qin G (2021) Efficiently backtesting conditional Value-at-Risk and conditional Expected Shortfall. J. Amer. Statist. Assoc. 116(536):2041–2052.Crossref, Google Scholar
• ter Schure J, Grünwald P (2021) ALL-IN meta-analysis: Breathing life into living systematic reviews. Preprint, submitted September 24, https://arxiv.org/abs/2109.12141.Google Scholar
• Ville J (1939) Étude critique de la notion de collectif. Thèses de l’entre-deux-guerres, no. 218 (Gauthier-Villars, Paris).Google Scholar
• Vovk V, Wang R (2021) E-values: Calibration, combination, and applications. Ann. Statist. 49(3):1736–1754.Crossref, Google Scholar
• Vovk V, Wang R (2024a) Merging sequential e-values via martingales. Electronic J. Statist. 18(1):1185–1205.Crossref, Google Scholar
• Vovk V, Wang R (2024b) Nonparametric e-tests of symmetry. New England J. Statist. Data Sci. 2(2):261–270.Crossref, Google Scholar
• Vovk V, Wang B, Wang R (2022) Admissible ways of merging p-values under arbitrary dependence. Ann. Statist. 50(1):351–375.Crossref, Google Scholar
• Wald A (1945) Sequential tests of statistical hypotheses. Ann. Math. Statist. 16(2):117–186.Crossref, Google Scholar
• Wang R, Ramdas A (2022) False discovery rate control with e-values. J. Royal Statist. Soc. Ser. B 84(3):822–852.Crossref, Google Scholar
• Wang R, Wei Y (2020) Risk functionals with convex level sets. Math. Finance 30(4):1337–1367.Crossref, Google Scholar
• Wang R, Zitikis R (2021) An axiomatic foundation for the Expected Shortfall. Management Sci. 67(3):1413–1429.Link, Google Scholar
• Wang R, Wei Y, Willmot GE (2020) Characterization, robustness and aggregation of signed Choquet integrals. Math. Oper. Res. 45(3):993–1015.Link, Google Scholar
• Wasserman L, Ramdas A, Balakrishnan S (2020) Universal inference. Proc. Natl. Acad. Sci. USA 117(29):16880–16890.Crossref, Google Scholar
• Waudby-Smith I, Ramdas A (2024) Estimating means of bounded random variables by betting. J. Royal Statist. Soc. Ser. B 86(1):1–27.Crossref, Google Scholar
• West KD (1996) Asymptotic inference about predictive ability. Econometrica 64(5):1067–1084.Crossref, Google Scholar
• Yaari ME (1987) The dual theory of choice under risk. Econometrica 55(1):95–115.Crossref, Google Scholar
• Ziegel JF (2016) Coherence and elicitability. Math. Finance 26(4):901–918.Crossref, Google Scholar
• Ziggel D, Berens T, Weiß GNF, Wied D (2014) A new set of improved Value-at-Risk backtests. J. Banking Finance 48:29–41.Crossref, Google Scholar