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Covariance function of vector self-similar processes

Author

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  • Lavancier, Frédéric
  • Philippe, Anne
  • Surgailis, Donatas

Abstract

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motions with correlated components having different self-similarity indices.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:23:p:2415-2421
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    References listed on IDEAS

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    1. 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.
    2. Maejima, Makoto & Mason, J. David, 1994. "Operator-self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 139-163, November.
    3. 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.
    4. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
    5. Stoev, Stilian A. & Taqqu, Murad S., 2006. "How rich is the class of multifractional Brownian motions?," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 200-221, February.
    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. Davidson, James & Hashimzade, Nigar, 2008. "Alternative Frequency And Time Domain Versions Of Fractional Brownian Motion," Econometric Theory, Cambridge University Press, vol. 24(1), pages 256-293, February.
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    Cited by:

    1. Li, Bao-Gen & Ling, Dian-Yi & Yu, Zu-Guo, 2021. "Multifractal temporally weighted detrended partial cross-correlation analysis of two non-stationary time series affected by common external factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    2. Tim Leung & Theodore Zhao, 2024. "A Noisy Fractional Brownian Motion Model for Multiscale Correlation Analysis of High-Frequency Prices," Mathematics, MDPI, vol. 12(6), pages 1-21, March.
    3. Gustavo Didier & Vladas Pipiras, 2012. "Exponents, Symmetry Groups and Classification of Operator Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 25(2), pages 353-395, June.
    4. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2010. "A two-sample test for comparison of long memory parameters," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2118-2136, October.
    5. Bao-Gen Li & Dian-Yi Ling & Zu-Guo Yu, 2020. "Multifractal temporally weighted detrended partial cross-correlation analysis to quantify intrinsic power-law cross-correlation of two non-stationary time series affected by common external factors," Papers 2006.09154, arXiv.org.
    6. 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.
    7. Wensheng Wang, 2024. "The Moduli of Continuity for Operator Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2097-2120, September.
    8. Ranieri Dugo & Giacomo Giorgio & Paolo Pigato, 2024. "The Multivariate Fractional Ornstein-Uhlenbeck Process," CEIS Research Paper 581, Tor Vergata University, CEIS, revised 28 Aug 2024.
    9. Martin Zubeldia & Michel Mandjes, 2021. "Large deviations for acyclic networks of queues with correlated Gaussian inputs," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 333-371, August.
    10. Characiejus, Vaidotas & Račkauskas, Alfredas, 2014. "Operator self-similar processes and functional central limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2605-2627.
    11. Davydov, Yu., 2012. "On convex hull of d-dimensional fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 37-39.

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