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Gaussian Semiparametric Estimation of Multivariate Fractionally Integrated Processes

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  • Katsumi Shimotsu

    ()
    (Queen's University)

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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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1062.pdf
File Function: First version 2006
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1062.

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Length: 39 pages
Date of creation: Feb 2006
Date of revision:
Publication status: Forthcoming in Journal of Econometrics
Handle: RePEc:qed:wpaper:1062

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Keywords: fractional integration; long memory; semiparametric estimation;

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References

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  1. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 535, University of Essex, Department of Economics.
  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. 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.
  5. Marc Henry & Paolo Zaffaroni, 2002. "The long range dependence paradigm for macroeconomics and finance," Discussion Papers 0102-19, Columbia University, Department of Economics.
  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.
  7. 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.
  8. 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.
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Citations

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Cited by:
  1. Peter C.B. Phillips, 2008. "Long Memory and Long Run Variation," Cowles Foundation Discussion Papers 1656, Cowles Foundation for Research in Economics, Yale University.
  2. Robinson, P.M., 2008. "Diagnostic testing for cointegration," Journal of Econometrics, Elsevier, vol. 143(1), pages 206-225, March.
  3. Ladislav Kristoufek, 2013. "Mixed-correlated ARFIMA processes for power-law cross-correlations," Papers 1307.6046, arXiv.org, revised Aug 2013.
  4. Shimotsu, Katsumi, 2010. "Exact Local Whittle Estimation of Fractionally Cointegrated Systems," Discussion Papers 2010-11, Graduate School of Economics, Hitotsubashi University.
  5. Manabu Asai & Michael McAleer, 2014. "Forecasting Co-Volatilities via Factor Models with Asymmetry and Long Memory in Realized Covariance," Tinbergen Institute Discussion Papers 14-037/III, Tinbergen Institute.
  6. 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.
  7. 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.
  8. Peter Robinson, 2007. "Diagnostic Testing For Cointegration," STICERD - Econometrics Paper Series /2007/522, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  9. 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.
  10. 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.
  11. Peter Robinson, 2007. "Diagnostic testing for cointegration," LSE Research Online Documents on Economics 4465, London School of Economics and Political Science, LSE Library.
  12. 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.
  13. Morten Ørregaard Nielsen & Per Frederiksen, 2008. "Fully Modified Narrow-Band Least Squares Estimation of Stationary Fractional Cointegration," Working Papers 1171, Queen's University, Department of Economics.

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