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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. 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(05), pages 621-642, October.
    2. Davidson, James & Hashimzade, Nigar, 2008. "Alternative Frequency And Time Domain Versions Of Fractional Brownian Motion," Econometric Theory, Cambridge University Press, vol. 24(01), pages 256-293, February.
    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(01), 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. Maejima, Makoto & Mason, J. David, 1994. "Operator-self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 139-163, November.
    6. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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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