Weak convergence of multivariate fractional processes
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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Volume (Year): 86 (2000)
Issue (Month): 1 (March)
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References listed on IDEAS
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- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
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