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Semiparametric Estimation of Fractional Cointegrating Subspaces

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Author Info

  • Willa Chen

    (Texas A&M University)

  • Clifford Hurvich

    (New York University)

Abstract

We consider a common components model for multivariate fractional cointegration, in which the s>=1 components have different memory parameters. The cointegrating rank is allowed to exceed 1. The true cointegrating vectors can be decomposed into orthogonal fractional cointegrating subspaces such that vectors from distinct subspaces yield cointegrating errors with distinct memory parameters, denoted by d_k for k=1,...,s. We estimate each cointegrating subsspace separately using appropriate sets of eigenvectors of an averaged periodogram matrix of tapered, differenced observations. The averaging uses the first m Fourier frequencies, with m fixed. We will show that any vector in the k'th estimated coingetraging subspace is, with high probability, close to the k'th true cointegrating subspace, in the sense that the angle between the estimated cointegrating vector and the true cointegrating subspace converges in probability to zero. The angle is O_p(n^{- \alpha_k}), where n is the sample size and \alpha_k is the shortest distance between the memory parameters corresponding to the given and adjacent subspaces. We show that the cointegrating residuals corresponding to an estimated cointegrating vector can be used to obtain a consistent and asymptotically normal estimate of the memory parameter for the given cointegrating subspace, using a univariate Gaussian semiparametric estimator with a bandwidth that tends to \infty more slowly than n. We also show how these memory parameter estimates can be used to test for fractional cointegration and to consistently identify the cointegrating subspaces.

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File URL: http://128.118.178.162/eps/em/papers/0412/0412007.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0412007.

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Length: 48 pages
Date of creation: 15 Dec 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0412007

Note: Type of Document - pdf; pages: 48
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Web page: http://128.118.178.162

Related research

Keywords: Fractional Cointegration; Long Memory; Tapering; Periodogram;

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References

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  1. J. A. Hausman, 1976. "Specification Tests in Econometrics," Working papers 185, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. D Marinucci & Peter M. Robinson, 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
  3. Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January.
  4. D Marinucci & Peter M Robinson, 2001. "Narrow-Band Analysis of Nonstationary Processes," STICERD - Econometrics Paper Series /2001/421, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
  6. Peter M Robinson & Yoshihiro Yajima, 2001. "Determination of Cointegrating Rank in Fractional Systems," STICERD - Econometrics Paper Series /2001/423, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  7. Gunderson, Brenda K. & Muirhead, Robb J., 1997. "On Estimating the Dimensionality in Canonical Correlation Analysis," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 121-136, July.
  8. Hurvich, Clifford M. & Moulines, Eric & Soulier, Philippe, 2002. "The FEXP estimator for potentially non-stationary linear time series," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 307-340, February.
  9. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  10. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, 05.
  11. 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.
  12. Chen, Willa W. & Hurvich, Clifford M., 2003. "Estimating fractional cointegration in the presence of polynomial trends," Journal of Econometrics, Elsevier, vol. 117(1), pages 95-121, November.
  13. D Marinucci & Peter Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 2015, London School of Economics and Political Science, LSE Library.
  14. D. Marinucci & Peter M. Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 303, London School of Economics and Political Science, LSE Library.
  15. Terrin, Norma & Hurvich, Clifford M., 1994. "An asymptotic Wiener-Itô representation for the low frequency ordinates of the periodogram of a long memory time series," Stochastic Processes and their Applications, Elsevier, vol. 54(2), pages 297-307, December.
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Citations

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Cited by:
  1. Hurvich, Clifford & Wang, Yi, 2009. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects," MPRA Paper 12575, University Library of Munich, Germany.
  2. Morten Ørregaard Nielsen, 2009. "Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders," CREATES Research Papers 2009-02, School of Economics and Management, University of Aarhus.
  3. repec:ise:isegwp:wp182008 is not listed on IDEAS
  4. Gil-Alana, L.A., 2008. "Testing of seasonal integration and cointegration with fractionally integrated techniques: An application to the Danish labour demand," Economic Modelling, Elsevier, vol. 25(2), pages 326-339, March.
  5. Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, School of Economics and Management, University of Aarhus.
  6. Javier Hualde, 2012. "Estimation of the cointegrating rank in fractional cointegration," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1205, Departamento de Economía - Universidad Pública de Navarra.
  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. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
  9. Katsumi Shimotsu & Morten Ørregaard 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.
  10. 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.
  11. Avarucci, Marco & Velasco, Carlos, 2008. "A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems," Research Memorandum 049, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  12. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus.

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