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Gaussian semiparametric estimation of multivariate fractionally integrated processes

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  • Katsumi Shimotsu

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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.

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Bibliographic Info

Paper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 571.

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Date of creation: 25 Nov 2003
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Handle: RePEc:esx:essedp:571

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  1. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Cowles Foundation Discussion Papers 1367, Cowles Foundation for Research in Economics, Yale University, revised Jul 2004.
  2. Lobato, Ignacio N & Robinson, Peter M, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 475-95, July.
  3. Brunetti, Celso & Gilbert, Christopher L., 2000. "Bivariate FIGARCH and fractional cointegration," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 509-530, December.
  4. Marc Henry & Paolo Zaffaroni, 2002. "The long range dependence paradigm for macroeconomics and finance," Discussion Papers 0102-19, Columbia University, Department of Economics.
  5. 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.
  6. 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 410-27, October.
  7. 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.
  8. 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.
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Citations

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Cited by:
  1. Shimotsu, Katsumi, 2010. "Exact Local Whittle Estimation of Fractionally Cointegrated Systems," Discussion Papers 2010-11, Graduate School of Economics, Hitotsubashi University.
  2. Morten ├śrregaard Nielsen & Per Frederiksen, 2008. "Fully Modified Narrow-Band Least Squares Estimation of Stationary Fractional Cointegration," Working Papers 1171, Queen's University, Department of Economics.
  3. Phillips, Peter C.B., 2009. "Long memory and long run variation," Journal of Econometrics, Elsevier, vol. 151(2), pages 150-158, August.
  4. Robinson, P.M., 2008. "Diagnostic testing for cointegration," Journal of Econometrics, Elsevier, vol. 143(1), pages 206-225, March.
  5. Frank S. Nielsen, 2009. "Local Whittle estimation of multivariate fractionally integrated processes," CREATES Research Papers 2009-38, School of Economics and Management, University of Aarhus.
  6. Peter M Robinson, 2007. "Multiple Local Whittle Estimation in StationarySystems," STICERD - Econometrics Paper Series /2007/525, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  7. Ladislav Kristoufek, 2013. "Mixed-correlated ARFIMA processes for power-law cross-correlations," Papers 1307.6046, arXiv.org, revised Aug 2013.
  8. Do, Hung Xuan & Brooks, Robert Darren & Treepongkaruna, Sirimon, 2013. "Generalized impulse response analysis in a fractionally integrated vector autoregressive model," Economics Letters, Elsevier, vol. 118(3), pages 462-465.
  9. Peter Robinson, 2007. "Diagnostic Testing For Cointegration," STICERD - Econometrics Paper Series /2007/522, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. Peter Robinson, 2007. "Diagnostic testing for cointegration," LSE Research Online Documents on Economics 4465, London School of Economics and Political Science, LSE Library.
  11. Peter M. Robinson, 2007. "Multiple local whittle estimation in stationary systems," LSE Research Online Documents on Economics 4436, London School of Economics and Political Science, LSE Library.
  12. Philip Bertram & Robinson Kruse & Philipp Sibbertsen, 2013. "Fractional integration versus level shifts: the case of realized asset correlations," Statistical Papers, Springer, vol. 54(4), pages 977-991, November.

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