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Extrapolation of stable random fields

Author

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  • Karcher, Wolfgang
  • Shmileva, Elena
  • Spodarev, Evgeny

Abstract

In this paper, we discuss three extrapolation methods for α-stable random fields with α∈(1,2]. We justify them, giving proofs of the existence and uniqueness of the solutions for each method and providing sufficient conditions for path continuity. Two methods are based on minimizing the variability of the difference between the predictor and the theoretical value, whereas in the third approach we provide a new method that maximizes the covariation between these two quantities.

Suggested Citation

  • Karcher, Wolfgang & Shmileva, Elena & Spodarev, Evgeny, 2013. "Extrapolation of stable random fields," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 516-536.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:516-536
    DOI: 10.1016/j.jmva.2012.11.004
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    References listed on IDEAS

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    1. Molchanov, Ilya, 2009. "Convex and star-shaped sets associated with multivariate stable distributions, I: Moments and densities," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2195-2213, November.
    2. Cline, Daren B. H. & Brockwell, Peter J., 1985. "Linear prediction of ARMA processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 281-296, April.
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    Cited by:

    1. Ammy-Driss, Ayoub & Garcin, Matthieu, 2023. "Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    2. Fries, Sébastien, 2018. "Conditional moments of noncausal alpha-stable processes and the prediction of bubble crash odds," MPRA Paper 97353, University Library of Munich, Germany, revised Nov 2019.

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