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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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    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, vol. 190(1), pages 18-45.
    4. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.

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