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Fractional Invariance Principle

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  • Yuzo Hosoya

Abstract

. The paper presents a central limit theorem and an allied invariance theorem related to what Marinucci and Robinson [Journal of Statistics, Planning and Inference (1999) Vol. 21, pp. 111–122] termed type II fractional Brownian motion. To widen the applicability, their independent and identically distributed (i.i.d.) assumption for the innovation process is relaxed, allowing it to be mildly conditionally heteroscedastic and requiring the Martingale‐difference property only asymptotically. Additionally, the paper presents, for contrast, the weak convergence of the conventional partial sum process in a related set‐up.

Suggested Citation

  • Yuzo Hosoya, 2005. "Fractional Invariance Principle," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 463-486, May.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:3:p:463-486
    DOI: 10.1111/j.1467-9892.2004.00411.x
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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    Cited by:

    1. Ergemen, Yunus Emre & Velasco, Carlos, 2017. "Estimation of fractionally integrated panels with fixed effects and cross-section dependence," Journal of Econometrics, Elsevier, vol. 196(2), pages 248-258.
    2. Hualde, Javier & Nielsen, Morten Ørregaard, 2020. "Truncated Sum Of Squares Estimation Of Fractional Time Series Models With Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 36(4), pages 751-772, August.
    3. Yunus Emre Ergemen, 2022. "Parametric Estimation of Long Memory in Factor Models," CREATES Research Papers 2022-10, Department of Economics and Business Economics, Aarhus University.
    4. Yunus Emre Ergemen & Carlos Velasco, 2019. "Persistence Heterogeneity Testing in Panels with Interactive Fixed Effects," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(4), pages 573-589, July.
    5. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    6. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    7. Ergemen, Yunus Emre, 2023. "Parametric estimation of long memory in factor models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1483-1499.

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