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Gaussian semiparametric estimation of multivariate fractionally integrated processes

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  • Shimotsu, Katsumi

Abstract

This paper analyzes the semiparametric estimation of multivariate long-range dependent processes. The class of spectral densities considered includes multivariate fractionally integrated processes, which are not covered by the existing literature. This paper also establishes the consistency of the multivariate Gaussian semiparametric estimator, which has not been shown in the other works. Asymptotic normality of the multivariate Gaussian semiparametric estimator is also established, and the proposed estimator is shown to have a smaller limiting variance than the two-step Gaussian semiparametric estimator studied by Lobato (1999). Gaussianity is not assumed in the asymptotic theory.

Suggested Citation

  • Shimotsu, Katsumi, 2003. "Gaussian semiparametric estimation of multivariate fractionally integrated processes," Economics Discussion Papers 8870, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:8870
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    References listed on IDEAS

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    1. Brunetti, Celso & Gilbert, Christopher L., 2000. "Bivariate FIGARCH and fractional cointegration," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 509-530, December.
    2. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
    3. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 475-495.
    4. Brunetti, Celso & Gilbert, Christopher L., 2000. "Bivariate FIGARCH and fractional cointegration," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 509-530, December.
    5. Bollerslev, Tim & Wright, Jonathan H., 2000. "Semiparametric estimation of long-memory volatility dependencies: The role of high-frequency data," Journal of Econometrics, Elsevier, vol. 98(1), pages 81-106, September.
    6. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation for Research in Economics, Yale University, revised Sep 2003.
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