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Local Whittle estimation of multivariate fractionally integrated processes

  • Frank S. Nielsen

    ()

    (Aarhus University and CREATES)

This paper derives a semiparametric estimator of multivariate fractionally integrated processes covering both stationary and non-stationary values of d. We utilize the notion of the extended discrete Fourier transform and periodogram to extend the multivariate local Whittle estimator of Shimotsu (2007) to cover non-stationary values of d. We show consistency and asymptotic normality for d between -1/2 and infinity. A simulation study illustrates the performance of the proposed estimator for relevant sample sizes. Empirical justification of the proposed estimator is shown through an empirical analysis of log spot exchange rates. We find that the log spot exchange rates of Germany, United Kingdom, Japan, Canada, France, Italy, and Switzerland against the US Dollar for the period January 1974 until December 2001 are well decribed as I (1) processes.

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File URL: ftp://ftp.econ.au.dk/creates/rp/09/rp09_38.pdf
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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-38.

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Length: 30
Date of creation: 08 Sep 2009
Date of revision:
Handle: RePEc:aah:create:2009-38
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Katsumi Shimotsu & Morten ├śrregaard Nielsen, 2006. "Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach," Working Papers 1029, Queen's University, Department of Economics.
  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. V Dalla & L Giraitis & J Hidalgo, . "Consistent estimation of the memory parameter for nonlinear time series," Discussion Papers 05/17, Department of Economics, University of York.
  4. Katsumi Shimotsu, 2006. "Gaussian Semiparametric Estimation of Multivariate Fractionally Integrated Processes," Working Papers 1062, Queen's University, Department of Economics.
  5. Nielsen M.O., 2004. "Optimal Residual-Based Tests for Fractional Cointegration and Exchange Rate Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 331-345, July.
  6. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
  7. Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, 03.
  8. 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.
  9. 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.
  10. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, School of Economics and Management, University of Aarhus.
  11. repec:cep:stiecm:/2006/497 is not listed on IDEAS
  12. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, 05.
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