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Extremal behaviour of models with multivariate random recurrence representation

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  • Klüppelberg, Claudia
  • Pergamenchtchikov, Serguei

Abstract

For the solution Y of a multivariate random recurrence model Yn=AnYn-1+[zeta]n in we investigate the extremal behaviour of the process , , for with z*=1. This extends results for positive matrices An. Moreover, we obtain explicit representations of the compound Poisson limit of point processes of exceedances over high thresholds in terms of its Poisson intensity and its jump distribution, which represents the cluster behaviour of such models on high levels. As a principal example we investigate a random coefficient autoregressive process.

Suggested Citation

  • Klüppelberg, Claudia & Pergamenchtchikov, Serguei, 2007. "Extremal behaviour of models with multivariate random recurrence representation," Stochastic Processes and their Applications, Elsevier, vol. 117(4), pages 432-456, April.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:4:p:432-456
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    References listed on IDEAS

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    1. Borkovec, Milan, 2000. "Extremal behavior of the autoregressive process with ARCH(1) errors," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 189-207, February.
    2. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    3. de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August.
    4. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
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    Cited by:

    1. Nielsen, Heino Bohn & Rahbek, Anders, 2014. "Unit root vector autoregression with volatility induced stationarity," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 144-167.
    2. Withers, Christopher S. & Nadarajah, Saralees, 2014. "The distribution of the maximum of the multivariate AR(p) and multivariate MA(p) processes," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 48-56.

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