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Original Articles

Where does the tail begin? An approach based on scoring rules

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References

  • Beirlant, J., Dierckx, G., Goegebeur, Y., Matthys, G. (1999). Burr regression and portfolio segmentation. Extremes 2(2):177–200. doi:10.1023/A:1009975020370
  • Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J. (2004). Statistics of Extremes. Chichester: Wiley.
  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31(3):307–327. doi:10.1016/0304-4076(86)90063-1
  • Bosma, J. J., Koetter, M., Wedow, M. (2019). Too connected to fail? Inferring network ties from price co-movements. Journal of Business & Economic Statistics 37:67–80. doi:10.1080/07350015.2016.1272459
  • Bücher, A., Jäschke, S., Wied, D. (2015). Nonparametric tests for constant tail dependence with an application to energy and finance. Journal of Econometrics 187(1):154–168. doi:10.1016/j.jeconom.2015.02.002
  • Chan, N. H., Deng, S. J., Peng, L., Xia, Z. (2007). Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations. Journal of Econometrics 137:556–576. doi:10.1016/j.jeconom.2005.08.008
  • Chen, S. X., Tang, S. X. (2005). Nonparametric inference of value-at-risk for dependent financial returns. Journal of Financial Econometrics 3(2):227–255. doi:10.1093/jjfinec/nbi012
  • Clauset, A., Shalizi, C. R., Newman, M. (2009). Power-law distributions in empirical data. SIAM Review 51(4):661–703. doi:10.1137/070710111
  • Csörgő, S., Deheuvels, P., Mason, D. (1985). Kernel estimates of the tail index of a distribution. The Annals of Statistics 13:1050–1077. doi:10.1214/aos/1176349656
  • Dacarogna, M. M., Gençay, R., Müller, U. A., Olsen, R. B., Pictet, O. V. (2001). An Introduction to High-Frequency Finance. San Diego: Academic Press.
  • Daníelsson, J., de Haan, L., Ergun, L. M., de Vries, C. G. (2016). Tail index estimation: Quantile driven threshold selection. Available at SSRN: http://dx.doi.org/10.2139/ssrn.2717478.
  • Danielsson, J., de Haan, L., Peng, L., de Vries, C. G. (2001). Using a bootstrap method to choose the sample fraction in tail index estimation. Journal of Multivariate Analysis 76(2):226–248. doi:10.1006/jmva.2000.1903
  • Davis, R. A., Mikosch, T. (1998). The sample autocorrelations of heavy-tailed processes with applications to ARCH. The Annals of Statistics 26:2049–2080. doi:10.1214/aos/1024691368
  • de Haan, L., Ferreira, A. (2006). Extreme Value Theory. New York: Springer.
  • Dey, D. K., Yan, J., eds. (2016). Extreme Value Modeling and Risk Analysis: Methods and Applications. Boca Raton: Chapman & Hall.
  • Diebold, F. X., Mariano, R. S. (1995). Comparing predictive accuracy. Journal of Business & Economic Statistics 13:253–263. doi:10.2307/1392185
  • Drees, H. (1995). Refined pickands estimators for the extreme value index. The Annals of Statistics 23:2059–2080. doi:10.1214/aos/1034713647
  • Drees, H. (2003). Extreme quantile estimation for dependent data, with applications to finance. Bernoulli 9(4):617–657. doi:10.3150/bj/1066223272
  • Drees, H., Janßen, A., Resnick, S. I., Wang, T. (2018). On a minimum distance procedure for threshold selection in tail analysis. arXiv e-Prints arXiv1811:06433.
  • Drees, H., Kaufmann, E. (1998). Selecting the optimal sample fraction in univariate extreme value estimation. Stochastic Processes and Their Applications 75(2):149–172. doi:10.1016/S0304-4149(98)00017-9
  • Embrechts, P., Klüppelberg, C., Mikosch, T. (1997). Modelling Extremal Events. Berlin: Springer.
  • Embrechts, P., Lindskog, F., McNeil, A. (2003). Modelling dependence with copulas and applications to risk management. In: Rachev, S. T. ed., Handbook of Heavy Tailed Distributions in Finance, Vol. 1 of Handbooks in Finance. Amsterdam: North-Holland, pp. 329–384.
  • Fagiolo, G., Napoletano, M., Roventini, A. (2008). Are output growth-rate distributions fat-tailed? some evidence from OECD countries. Journal of Applied Econometrics 23(5):639–669. doi:10.1002/jae.1003
  • Francq, C., Zakoïan, J. M. (2010). GARCH Models: Structure, Statistical Inference and Financial Applications. Chichester: Wiley.
  • Gabaix, X. (1999). Zipf’s law for cities: An explanation. The Quarterly Journal of Economics 114(3):739–767. doi:10.1162/003355399556133
  • Gabaix, X. (2009). Power laws in economics and finance. Annual Review of Economics 1(1):255–293. doi:10.1146/annurev.economics.050708.142940
  • Gabaix, X., Gopikrishnan, P., Plerou, V., Stanley, H. E. (2006). Institutional investors and stock market volatility. The Quarterly Journal of Economics 121(2):461–504. doi:10.1162/qjec.2006.121.2.461
  • Gabaix, X., Ibragimov, R. (2011). Rank – 1/2: A simple way to improve the OLS estimation of tail exponents. Journal of Business & Economic Statistics 29:24–39. doi:10.1198/jbes.2009.06157
  • Gneiting, T. (2011). Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746–762. doi:10.1198/jasa.2011.r10138
  • Gneiting, T., Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102(477):359–378. doi:10.1198/016214506000001437
  • Gneiting, T., Ranjan, R. (2011). Comparing density forecasts using threshold- and quantile-weighted scoring rules. Journal of Business & Economic Statistics 29:411–422. doi:10.1198/jbes.2010.08110
  • Gonzalo, J., Olmo, J. (2004). Which extreme values are really extreme? Journal of Financial Econometrics 2(3):349–369. doi:10.1093/jjfinec/nbh014
  • Gu, Z., Ibragimov, R. (2018). The “cubic law of the stock returns” in emerging markets. Journal of Empirical Finance 46:182–190. doi:10.1016/j.jempfin.2017.11.008
  • Gupta, A., Liang, B. (2005). Do hedge funds have enough Capital? A value-at-risk approach. Journal of Financial Economics 77(1):219–253. doi:10.1016/j.jfineco.2004.06.005
  • Hartmann, P., Straetmans, S., de Vries, C. G. (2006). Banking system stability: A cross-atlantic perspective. In: Carey, M., Stulz, R. M., eds., The Risks of Financial Institutions. Chicago and London: The University of Chicago Press, 1st edn., pp. 133–193.
  • Heffernan, J. E. (2000). A directory of coefficients of tail dependence. Extremes 3(3):279–290.
  • Hill, B. (1975). A simple general approach to inference about the tail of a distribution. The Annals of Statistics 3(5):1163–1174. doi:10.1214/aos/1176343247
  • Hill, J. B. (2010). On tail index estimation for dependent, heterogeneous data. Econometric Theory 26(5):1398–1436. doi:10.1017/S0266466609990624
  • Hill, J. B. (2015). Expected shortfall estimation and gaussian inference for infinite variance time series. Journal of Financial Econometrics 13(1):1–44. doi:10.1093/jjfinec/nbt020
  • Hoga, Y. (2017). Change point tests for the tail index of β-mixing random variables. Econometric Theory 33(4):915–954. doi:10.1017/S0266466616000189
  • Hoga, Y. (2018a). Detecting tail risk differences in multivariate time series. Journal of Time Series Analysis 39(5):665–689. doi:10.1111/jtsa.12292
  • Hoga, Y. (2018b). A structural break test for extremal dependence in β-mixing random vectors. Biometrika 105(3):627–643. doi:10.1093/biomet/asy030
  • Hoga, Y. (2019a). Confidence intervals for conditional tail risk measures in ARMA–GARCH models. Journal of Business & Economic Statistics 37:613–624. doi:10.1080/07350015.2017.1401543
  • Hoga, Y. (2019b). Extreme conditional tail moment estimation under serial dependence. Journal of Financial Econometrics 17(4):587–615. doi:10.1093/jjfinec/nby016
  • Holzmann, H., Klar, B. (2017). Discussion of “Elicitability and backtesting: Perspectives for banking regulation”. The Annals of Applied Statistics 11(4):1875–1882. doi:10.1214/17-AOAS1041A
  • Hua, L., Joe, H. (2011). Second order regular variation and conditional tail expectation of multiple risks. Insurance: Mathematics and Economics 49:537–546. doi:10.1016/j.insmatheco.2011.08.013
  • Huber, P. J., Ronchetti, E. M. (2009). Robust Statistics, 2nd edn. Hoboken: Wiley.
  • Jalal, A., Rockinger, M. (2008). Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data. Journal of Empirical Finance 15(5):868–877. doi:10.1016/j.jempfin.2008.02.004
  • Koenker, R., Bassett, G. (1978). Regression quantiles. Econometrica 46(1):33–50. doi:10.2307/1913643
  • Kuester, K., Mittnik, S., Paolella, M. S. (2006). Value-at-risk prediction: A comparison of alternative strategies. Journal of Financial Econometrics 4(1):53–89. doi:10.1093/jjfinec/nbj002
  • Laurini, F., Tawn, J. A. (2008). Regular variation and extremal dependence of GARCH residuals with application to market risk measures. Econometric Reviews 28(1–3):146–169. doi:10.1080/07474930802387985
  • Ledford, A. W., Tawn, J. A. (1996). Statistics for near independence in multivariate extreme values. Biometrika 83(1):169–187. doi:10.1093/biomet/83.1.169
  • Ledford, A. W., Tawn, J. A. (1997). Modelling dependence within joint tail regions. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 59(2):475–499. doi:10.1111/1467-9868.00080
  • Longin, F., ed. (2017). Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications. Hoboken: Wiley.
  • McNeil, A. J., Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach. Journal of Empirical Finance 7(3–4):271–300. doi:10.1016/S0927-5398(00)00012-8
  • Mikosch, T., Stărică, C. (2000). Limit theory for the sample autocorrelations and extremes of a GARCH(1,1) process. The Annals of Statistics 28:1427–1451. doi:10.1214/aos/1015957401
  • Müller, U. K., Wang, Y. (2017). Fixed-k asymptotic inference about tail properties. Journal of the American Statistical Association 112(519):1334–1343. doi:10.1080/01621459.2016.1215990
  • Nolde, N., Zhang, J. (2019). Conditional extremes in asymmetric financial markets. Journal of Business & Economic Statistics 0:1–13. doi:10.1080/07350015.2018.1476248
  • Novak, S., Beirlant, J. (2006). The magnitude of a market crash can be predicted. Journal of Banking & Finance 30:453–462. doi:10.1016/j.jbankfin.2005.04.023
  • Pickands, J. (1975). Statistical inference using extreme order statistics. The Annals of Statistics 3:119–131.
  • Poon, S. H., Rockinger, M., Tawn, J. (2004). Extreme value dependence in financial markets: Diagnostics, models, and financial implications. Review of Financial Studies 17(2):581–610. doi:10.1093/rfs/hhg058
  • Quintos, C., Fan, Z., Philips, P. C. B. (2001). Structural change tests in tail behaviour and the asian crisis. Review of Economic Studies 68(3):633–663. doi:10.1111/1467-937X.00184
  • Resnick, S. (2007). Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. New York: Springer.
  • Resnick, S., Stărică, C. (1997). Smoothing the hill estimator. Advances in Applied Probability 29(1):271–293. doi:10.2307/1427870
  • Sibuya, M. (1960). Bivariate extreme statistics. Annals of the Institute of Statistical Mathematics 11(3):195–210. doi:10.1007/BF01682329
  • Straetmans, S., Chaudhry, S. M. (2015). Tail risk and systemic risk of US and eurozone financial institutions in the wake of the global financial crisis. Journal of International Money and Finance 58:191–223. doi:10.1016/j.jimonfin.2015.07.003
  • Straetmans, S. T. M., Verschoor, W. F. C., Wolff, C. (2008). Extreme US stock market fluctuations in the wake of 9/11. Journal of Applied Econometrics 23(1):17–42. doi:10.1002/jae.973
  • Sun, P., de Vries, C. G. (2018). Exploiting tail shape biases to discriminate between stable and student t alternatives. Journal of Applied Econometrics 33(5):708–726. doi:10.1002/jae.2628
  • 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 37:121–133. doi:10.1080/07350015.2017.1281815
  • Trapani, L. (2016). Testing for (in)finite moments. Journal of Econometrics 191(1):57–68. doi:10.1016/j.jeconom.2015.08.006
  • Wagner, N., Marsh, T. A. (2005). Measuring tail thickness under GARCH and an application to extreme exchange rate changes. Journal of Empirical Finance 12(1):165–185. doi:10.1016/j.jempfin.2003.11.002
  • Weissman, I. (1978). Estimation of parameters and large quantiles based on the k largest observations. Journal of the American Statistical Association 73:812–815. doi:10.2307/2286285
  • Ziegel, J. F., Krüger, F., Jordan, A., Fasciati, F. (2019). Robust forecast evaluation of expected shortfall. Journal of Financial Econometrics 1–26. doi:10.1093/jjfinec/nby035

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