IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1809.02303.html
   My bibliography  Save this paper

Change-Point Testing for Risk Measures in Time Series

Author

Listed:
  • Lin Fan
  • Peter W. Glynn
  • Markus Pelger

Abstract

We propose novel methods for change-point testing for nonparametric estimators of expected shortfall and related risk measures in weakly dependent time series. We can detect general multiple structural changes in the tails of marginal distributions of time series under general assumptions. Self-normalization allows us to avoid the issues of standard error estimation. The theoretical foundations for our methods are functional central limit theorems, which we develop under weak assumptions. An empirical study of S&P 500 and US Treasury bond returns illustrates the practical use of our methods in detecting and quantifying market instability via the tails of financial time series.

Suggested Citation

  • Lin Fan & Peter W. Glynn & Markus Pelger, 2018. "Change-Point Testing for Risk Measures in Time Series," Papers 1809.02303, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:1809.02303
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1809.02303
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Moosup Kim & Sangyeol Lee, 2011. "Change point test for tail index for dependent data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(3), pages 297-311, November.
    2. Sen, Pranab Kumar, 1972. "On the Bahadur representation of sample quantiles for sequences of [phi]-mixing random variables," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 77-95, March.
    3. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
    4. Hoga, Yannick, 2017. "Change Point Tests For The Tail Index Of Β-Mixing Random Variables," Econometric Theory, Cambridge University Press, vol. 33(4), pages 915-954, August.
    5. Deng, Ai & Perron, Pierre, 2008. "A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change," Journal of Econometrics, Elsevier, vol. 142(1), pages 212-240, January.
    6. Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(1), pages 87-107, Winter.
    7. Bucher, Axel, 2015. "A Note on Weak Convergence of the Sequential Multivariate Empirical Process Under Strong Mixing," LIDAM Reprints ISBA 2015042, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Jonathan El Methni & Laurent Gardes & Stéphane Girard, 2014. "Non-parametric Estimation of Extreme Risk Measures from Conditional Heavy-tailed Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 988-1012, December.
    9. Xu, Ke-Li, 2016. "Model-Free Inference For Tail Risk Measures," Econometric Theory, Cambridge University Press, vol. 32(1), pages 122-153, February.
    10. Xiaofeng Shao, 2010. "A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366, June.
    11. Qu, Zhongjun, 2008. "Testing for structural change in regression quantiles," Journal of Econometrics, Elsevier, vol. 146(1), pages 170-184, September.
    12. Song Xi Chen, 2005. "Nonparametric Inference of Value-at-Risk for Dependent Financial Returns," Journal of Financial Econometrics, Oxford University Press, vol. 3(2), pages 227-255.
    13. Wendler, Martin, 2011. "Bahadur representation for U-quantiles of dependent data," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1064-1079, July.
    14. Shao, Xiaofeng & Zhang, Xianyang, 2010. "Testing for Change Points in Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1228-1240.
    15. Marco Rocco, 2014. "Extreme Value Theory In Finance: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 28(1), pages 82-108, February.
    16. Lee Schruben, 1983. "Confidence Interval Estimation Using Standardized Time Series," Operations Research, INFORMS, vol. 31(6), pages 1090-1108, December.
    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. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.

    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. Hong, Yongmiao & Linton, Oliver & McCabe, Brendan & Sun, Jiajing & Wang, Shouyang, 2024. "Kolmogorov–Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach," Journal of Econometrics, Elsevier, vol. 238(2).
    2. Kim, Seonjin & Zhao, Zhibiao & Shao, Xiaofeng, 2015. "Nonparametric functional central limit theorem for time series regression with application to self-normalized confidence interval," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 277-290.
    3. Aigner, Maximilian & Chavez-Demoulin, Valérie & Guillou, Armelle, 2022. "Measuring and comparing risks of different types," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 1-21.
    4. Yi-Ting Chen & Zhongjun Qu, 2015. "M Tests with a New Normalization Matrix," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 617-652, May.
    5. Christis Katsouris, 2023. "Structural Break Detection in Quantile Predictive Regression Models with Persistent Covariates," Papers 2302.05193, arXiv.org.
    6. Sun, Jiajing & Hong, Yongmiao & Linton, Oliver & Zhao, Xiaolu, 2022. "Adjusted-range self-normalized confidence interval construction for censored dependent data," Economics Letters, Elsevier, vol. 220(C).
    7. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    8. Guangwu Liu & Liu Jeff Hong, 2009. "Kernel estimation of quantile sensitivities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 511-525, September.
    9. Hoga, Yannick, 2017. "Monitoring multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 105-121.
    10. 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.
    11. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    12. Qinchi Zhang & Wenzhi Yang & Shuhe Hu, 2014. "On Bahadur representation for sample quantiles under α-mixing sequence," Statistical Papers, Springer, vol. 55(2), pages 285-299, May.
    13. Kai Wenger & Christian Leschinski & Philipp Sibbertsen, 2019. "Change-in-mean tests in long-memory time series: a review of recent developments," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 237-256, June.
    14. Jiang, Feiyu & Zhao, Zifeng & Shao, Xiaofeng, 2023. "Time series analysis of COVID-19 infection curve: A change-point perspective," Journal of Econometrics, Elsevier, vol. 232(1), pages 1-17.
    15. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    16. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Boston University - Department of Economics - Working Papers Series WP2019-02, Boston University - Department of Economics.
    17. Holger Dette & Kevin Kokot & Stanislav Volgushev, 2020. "Testing relevant hypotheses in functional time series via self‐normalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 629-660, July.
    18. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    19. Suparna Biswas & Santanu Dutta, 2015. "Assessing Market Risk of Indian Index Funds," Global Business Review, International Management Institute, vol. 16(3), pages 511-523, June.
    20. Bellini, Fabio & Fadina, Tolulope & Wang, Ruodu & Wei, Yunran, 2022. "Parametric measures of variability induced by risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 270-284.

    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:1809.02303. 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.