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Tail indices for $$\mathbf{A}\mathbf{X}+\mathbf{B}$$ A X + B Recursion with Triangular Matrices

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  • Muneya Matsui

    (Nanzan University)

  • Witold Świątkowski

    (University of Wrocław)

Abstract

We study multivariate stochastic recurrence equations (SREs) with triangular matrices. If coefficient matrices of SREs have strictly positive entries, the classical Kesten result says that the stationary solution is regularly varying and the tail indices are the same in all directions. This framework, however, is too restrictive for applications. In order to widen applicability of SREs, we consider SREs with triangular matrices and we prove that their stationary solutions are regularly varying with component-wise different tail exponents. Several applications to GARCH models are suggested.

Suggested Citation

  • Muneya Matsui & Witold Świątkowski, 2021. "Tail indices for $$\mathbf{A}\mathbf{X}+\mathbf{B}$$ A X + B Recursion with Triangular Matrices," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1831-1869, December.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:4:d:10.1007_s10959-020-01019-8
    DOI: 10.1007/s10959-020-01019-8
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    References listed on IDEAS

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    1. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    2. Fernández, Begoña & Muriel, Nelson, 2009. "Regular variation and related results for the multivariate GARCH(p,q) model with constant conditional correlations," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1538-1550, August.
    3. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    4. Sun, Pengfei & Zhou, Chen, 2014. "Diagnosing the distribution of GARCH innovations," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 287-303.
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