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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 is motivated by and includes those of multivariate fractionally integrated processes. The paper establishes the consistency of the multivariate Gaussian semiparametric estimator (GSE), which has not been shown in other work, and the asymptotic normality of the GSE estimator. The proposed GSE estimator is shown to have a smaller limiting variance than the two-step GSE estimator studied by Lobato (1999). Gaussianity is not assumed in the asymptotic theory. Some simulations confirm the relevance of the asymptotic results in samples of the size used in practical work.
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Suggested Citation

  • Shimotsu, Katsumi, 2007. "Gaussian semiparametric estimation of multivariate fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 137(2), pages 277-310, April.
  • Handle: RePEc:eee:econom:v:137:y:2007:i:2:p:277-310
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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 & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-427, October.
    3. 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.
    4. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 475-495.
    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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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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