IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.18643.html
   My bibliography  Save this paper

Tail Risk Analysis for Financial Time Series

Author

Listed:
  • Anna Kiriliouk
  • Chen Zhou

Abstract

This book chapter illustrates how to apply extreme value statistics to financial time series data. Such data often exhibits strong serial dependence, which complicates assessment of tail risks. We discuss the two main approches to tail risk estimation, unconditional and conditional quantile forecasting. We use the S&P 500 index as a case study to assess serial (extremal) dependence, perform an unconditional and conditional risk analysis, and apply backtesting methods. Additionally, the chapter explores the impact of serial dependence on multivariate tail dependence.

Suggested Citation

  • Anna Kiriliouk & Chen Zhou, 2024. "Tail Risk Analysis for Financial Time Series," Papers 2409.18643, arXiv.org.
  • Handle: RePEc:arx:papers:2409.18643
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.18643
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Natalia Nolde & Johanna F. Ziegel, 2016. "Elicitability and backtesting: Perspectives for banking regulation," Papers 1608.05498, arXiv.org, revised Feb 2017.
    2. P. Hartmann & S. Straetmans & C. G. de Vries, 2004. "Asset Market Linkages in Crisis Periods," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 313-326, February.
    3. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    4. Yannick Hoga, 2019. "Confidence Intervals for Conditional Tail Risk Measures in ARMA–GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 613-624, October.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. De Jonghe, Olivier, 2010. "Back to the basics in banking? A micro-analysis of banking system stability," Journal of Financial Intermediation, Elsevier, vol. 19(3), pages 387-417, July.
    7. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    8. Christopher A. T. Ferro & Johan Segers, 2003. "Inference for clusters of extreme values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 545-556, May.
    9. Laurens Haan & Cécile Mercadier & Chen Zhou, 2016. "Adapting extreme value statistics to financial time series: dealing with bias and serial dependence," Finance and Stochastics, Springer, vol. 20(2), pages 321-354, April.
    10. Axel Bücher & Peter N Posch & Philipp Schmidtke, 2020. "Using the Extremal Index for Value-at-Risk Backtesting," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 556-584.
    11. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    Full references (including those not matched with items on IDEAS)

    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. Hoga, Yannick, 2021. "The uncertainty in extreme risk forecasts from covariate-augmented volatility models," International Journal of Forecasting, Elsevier, vol. 37(2), pages 675-686.
    2. James, Robert & Leung, Henry & Leung, Jessica Wai Yin & Prokhorov, Artem, 2023. "Forecasting tail risk measures for financial time series: An extreme value approach with covariates," Journal of Empirical Finance, Elsevier, vol. 71(C), pages 29-50.
    3. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    4. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    5. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    6. Spierdijk, Laura, 2016. "Confidence intervals for ARMA–GARCH Value-at-Risk: The case of heavy tails and skewness," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 545-559.
    7. Ngozi G. Emenogu & Monday Osagie Adenomon & Nwaze Obini Nweze, 2020. "On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-25, December.
    8. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    9. Conrad, Christian & Mammen, Enno, 2016. "Asymptotics for parametric GARCH-in-Mean models," Journal of Econometrics, Elsevier, vol. 194(2), pages 319-329.
    10. H. Kaibuchi & Y. Kawasaki & G. Stupfler, 2022. "GARCH-UGH: a bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 22(7), pages 1277-1294, July.
    11. Javed Farrukh & Podgórski Krzysztof, 2017. "Tail Behavior and Dependence Structure in the APARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 9(2), pages 1-48, July.
    12. Oliver Linton & Dajing Shang & Yang Yan, 2012. "Efficient estimation of conditional risk measures in a semiparametric GARCH model," CeMMAP working papers 25/12, Institute for Fiscal Studies.
    13. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.
    14. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    15. Ha, Jeongcheol & Lee, Taewook, 2011. "NM-QELE for ARMA-GARCH models with non-Gaussian innovations," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 694-703, June.
    16. Preminger, Arie & Storti, Giuseppe, 2014. "Least squares estimation for GARCH (1,1) model with heavy tailed errors," MPRA Paper 59082, University Library of Munich, Germany.
    17. 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.
    18. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    19. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, October.
    20. Santos, Douglas G. & Candido, Osvaldo & Tófoli, Paula V., 2022. "Forecasting risk measures using intraday and overnight information," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).

    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:2409.18643. 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.