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Heavy tailed time series with extremal independence

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  • Rafal Kulik
  • Philippe Soulier
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    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. Theory is illustrated by numerical studies and data analysis.

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    File URL: http://arxiv.org/pdf/1307.1501
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    Paper provided by arXiv.org in its series Papers with number 1307.1501.

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    Date of creation: Jul 2013
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    Handle: RePEc:arx:papers:1307.1501

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    1. Gourieroux, Christian & Robert, Christian Y., 2006. "Stochastic Unit Root Models," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1052-1090, December.
    2. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    3. 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.
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