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Estimation Of And Inference About The Expected Shortfall For Time Series With Infinite Variance

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  • Linton, Oliver
  • Xiao, Zhijie

Abstract

We study estimation and inference of the expected shortfall for time series with infinite variance. Both the smoothed and nonsmoothed estimators are investigated. The rate of convergence is determined by the tail thickness parameter, and the limiting distribution is in the stable class with parameters depending on the tail thickness parameter of the time series and on the dependence structure, which makes inference complicated. A subsampling procedure is proposed to carry out statistical inference. We also analyze a nonparametric estimator of the conditional expected shortfall. A Monte Carlo experiment is conducted to evaluate the finite sample performance of the proposed inference procedure, and an empirical application to emerging market exchange rates (from October 1997 to October 2008) is conducted to highlight the proposed study.

Suggested Citation

  • Linton, Oliver & Xiao, Zhijie, 2013. "Estimation Of And Inference About The Expected Shortfall For Time Series With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 29(04), pages 771-807, August.
  • Handle: RePEc:cup:etheor:v:29:y:2013:i:04:p:771-807_00
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    1. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, pages 325-353.
    2. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests Structural Change in First-Order Dynamic Models," Cahiers de recherche 9548, Universite de Montreal, Departement de sciences economiques.
    3. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, pages 556-576.
    4. Chambers, MJ, 2010. "Jackknife Estimation of Stationary Autoregressive Models," Economics Discussion Papers 2786, University of Essex, Department of Economics.
    5. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, pages 2213-2227.
    6. Moshe Buchinsky & Denis Fougère & Francis Kramarz & Rusty Tchernis, 2002. "Interfirm Mobility, Wages and the Returns to Seniority and Experience in the U.S," Working Papers 2002-29, Center for Research in Economics and Statistics.
    7. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, pages 142-157.
    8. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, pages 391-407.
    9. Escanciano, J. Carlos & Olmo, Jose, 2010. "Backtesting Parametric Value-at-Risk With Estimation Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 36-51.
    10. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, pages 325-353.
    11. Bao, Yong & Ullah, Aman, 2004. "Bias of a Value-at-Risk estimator," Finance Research Letters, Elsevier, pages 241-249.
    12. J. Carlos Escanciano & Jose Olmo, 2011. "Robust Backtesting Tests for Value-at-risk Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 132-161, Winter.
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    Cited by:

    1. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org.
    2. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.
    3. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, pages 18-45.
    4. Hill, Jonathan B. & Prokhorov, Artem, 2015. "GEL Estimation for Heavy-Tailed GARCH Models with Robust Empirical Likelihood Inference," Working Papers 2015-03, University of Sydney Business School, Discipline of Business Analytics.
    5. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, pages 57-68.

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