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Multivariate linear recursions with Markov-dependent coefficients

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  • Hay, Diana
  • Rastegar, Reza
  • Roitershtein, Alexander

Abstract

We study a linear recursion with random Markov-dependent coefficients. In a "regular variation in, regular variation out" setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results previously established for i.i.d. coefficients.

Suggested Citation

  • Hay, Diana & Rastegar, Reza & Roitershtein, Alexander, 2011. "Multivariate linear recursions with Markov-dependent coefficients," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 521-527, March.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:521-527
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    References listed on IDEAS

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    1. 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.
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    5. Ghosh, Arka P. & Hay, Diana & Hirpara, Vivek & Rastegar, Reza & Roitershtein, Alexander & Schulteis, Ashley & Suh, Jiyeon, 2010. "Random linear recursions with dependent coefficients," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1597-1605, November.
    6. Stelzer, Robert, 2008. "Multivariate Markov-switching ARMA processes with regularly varying noise," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1177-1190, July.
    7. Engle, Robert F. (ed.), 1995. "ARCH: Selected Readings," OUP Catalogue, Oxford University Press, number 9780198774327.
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    Cited by:

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    3. Jie Cai & Nan Li, 2019. "Growth Through Inter-sectoral Knowledge Linkages," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 1827-1866.

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