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Heavy tailed time series with extremal independence

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  • Rafal Kulik
  • Philippe Soulier

Abstract

We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information about limiting behavior of time series with extremal independence by introducing a sequence of scaling functions and conditional scaling exponent. Both quantities provide more information about joint extremes than a widely used tail dependence coefficient. We calculate the scaling functions and the scaling exponent for variety of models, including Markov chains, exponential autoregressive model, stochastic volatility with heavy tailed innovations or volatility.

Suggested Citation

  • Rafal Kulik & Philippe Soulier, 2013. "Heavy tailed time series with extremal independence," Papers 1307.1501, arXiv.org, revised Oct 2014.
    • Handle: RePEc:arx:papers:1307.1501
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    References listed on IDEAS

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    1. Gourieroux, Christian & Robert, Christian Y., 2006. "Stochastic Unit Root Models," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1052-1090, December.
    2. Rootzén, Holger, 2009. "Weak convergence of the tail empirical process for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 468-490, February.
    3. janssen, Anja & Segers, Johan, 2013. "Markov Tail Chains," LIDAM Discussion Papers ISBA 2013017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Kulik, Rafal & Soulier, Philippe, 2011. "The tail empirical process for long memory stochastic volatility sequences," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 109-134, January.
    5. Basrak, Bojan & Segers, Johan, 2009. "Regularly varying multivariate time series," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1055-1080, April.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Cited by:

    1. Segers, Johan & Zhao, Yuwei & Meinguet, Thomas, 2016. "Radial-angular decomposition of regularly varying time series in star-shaped metric spaces," LIDAM Discussion Papers ISBA 2016017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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