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Limit theorems in the context of multivariate long-range dependence

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  • Düker, Marie-Christine

Abstract

This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated, paying special attention to the mixed cases of short- and long-range dependent series. The resulting limit processes can involve multivariate Brownian motion marginals, operator fractional Brownian motions and matrix-valued versions of the so-called Rosenblatt process.

Suggested Citation

  • Düker, Marie-Christine, 2020. "Limit theorems in the context of multivariate long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5394-5425.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5394-5425
    DOI: 10.1016/j.spa.2020.03.011
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    References listed on IDEAS

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    1. Bai, Shuyang & Taqqu, Murad S., 2013. "Multivariate limits of multilinear polynomial-form processes with long memory," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2473-2485.
    2. Laha, R. G. & Rohatgi, V. K., 1981. "Operator self similar stochastic processes in," Stochastic Processes and their Applications, Elsevier, vol. 12(1), pages 73-84, October.
    3. Stefanos Kechagias & Vladas Pipiras, 2015. "Definitions And Representations Of Multivariate Long-Range Dependent Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 1-25, January.
    4. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2009. "Covariance function of vector self-similar processes," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2415-2421, December.
    5. Pipiras,Vladas & Taqqu,Murad S., 2017. "Long-Range Dependence and Self-Similarity," Cambridge Books, Cambridge University Press, number 9781107039469, October.
    6. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    7. Chung, Ching-Fan, 2002. "Sample Means, Sample Autocovariances, And Linear Regression Of Stationary Multivariate Long Memory Processes," Econometric Theory, Cambridge University Press, vol. 18(1), pages 51-78, February.
    8. Shuyang Bai & Murad S. Taqqu, 2013. "Multivariate Limit Theorems In The Context Of Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 717-743, November.
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