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Weak convergence of multivariate fractional processes

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  • Marinucci, D.
  • Robinson, P. M.
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    Abstract

    Weak convergence to a form of fractional Brownian motion is established for a wide class of nonstationary fractionally integrated multivariate processes. Instrumental for the main argument is a result of some independent interest on approximations for partial sums of stationary linear vector sequences. A functional central limit theorem for smoothed processes is established under more general assumptions.

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    File URL: http://www.sciencedirect.com/science/article/B6V1B-3YJ9Y7K-5/2/9f9e800563495d183ad1e50acc3f88ee
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 86 (2000)
    Issue (Month): 1 (March)
    Pages: 103-120

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    Handle: RePEc:eee:spapps:v:86:y:2000:i:1:p:103-120

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    Keywords: Nonstationary fractional integration Functional central limit theorem;

    References

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    1. Kokoszka, P. & Mikosch, T., 1997. "The integrated periodogram for long-memory processes with finite or infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 55-78, February.
    2. Giraitis, Liudas & Koul, Hira, 1997. "Estimation of the dependence parameter in linear regression with long-range-dependent errors," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 207-224, November.
    3. Csörgo, Sándor & Mielniczuk, Jan, 1995. "Distant long-range dependent sums and regression estimation," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 143-155, September.
    4. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
    5. Einmahl, Uwe, 1989. "Extensions of results of Komlós, Major, and Tusnády to the multivariate case," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 20-68, January.
    6. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
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