=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."> =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."> =1 components have different memory parameters. The cointegrating rank is allowed to exceed 1. The true ">
[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpem/0412007.html
   My bibliography  Save this paper

Semiparametric Estimation of Fractional Cointegrating Subspaces

Author

Listed:
  • 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.

Suggested Citation

  • Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0412007
    Note: Type of Document - pdf; pages: 48
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0412/0412007.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    2. Marinucci, D. & Robinson, Peter M., 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 303, London School of Economics and Political Science, LSE Library.
    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. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    5. 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.
    6. 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.
    7. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    8. Marinucci, D & Robinson, Peter M., 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
    9. Marinucci, D & Robinson, Peter, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 2015, London School of Economics and Political Science, LSE Library.
    10. Clifford M. Hurvich & Willa W. Chen, 2000. "An Efficient Taper for Potentially Overdifferenced Long‐memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(2), pages 155-180, March.
    11. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
    12. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series 420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. 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.
    14. 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.
    15. 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.
    16. D Marinucci & Peter M Robinson, 2001. "Narrow-Band Analysis of Nonstationary Processes," STICERD - Econometrics Paper Series 421, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    17. Carlos Velasco, 2003. "Gaussian Semi‐parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nielsen, Morten Ørregaard, 2010. "Nonparametric cointegration analysis of fractional systems with unknown integration orders," Journal of Econometrics, Elsevier, vol. 155(2), pages 170-187, April.
    2. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    3. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    4. Hurvich, Cliiford & Wang, Yi, 2006. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects," MPRA Paper 1413, University Library of Munich, Germany.
    5. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.
    6. Morten Ø. Nielsen & Per Houmann Frederiksen, 2008. "Fully Modified Narrow-band Least Squares Estimation Of Stationary Fractional Cointegration," Working Paper 1171, Economics Department, Queen's University.
    7. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    8. 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.
    9. Avarucci, Marco & Velasco, Carlos, 2009. "A Wald test for the cointegration rank in nonstationary fractional systems," Journal of Econometrics, Elsevier, vol. 151(2), pages 178-189, August.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    2. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, vol. 133(1), pages 343-371, July.
    3. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    4. Hurvich, Cliiford & Wang, Yi, 2006. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects," MPRA Paper 1413, University Library of Munich, Germany.
    5. Morten Ø. Nielsen & Per Houmann Frederiksen, 2008. "Fully Modified Narrow-band Least Squares Estimation Of Stationary Fractional Cointegration," Working Paper 1171, Economics Department, Queen's University.
    6. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    7. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    8. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 263-298.
    9. Hualde, Javier, 2006. "Unbalanced Cointegration," Econometric Theory, Cambridge University Press, vol. 22(5), pages 765-814, October.
    10. Hualde, J. & Robinson, P.M., 2007. "Root-n-consistent estimation of weak fractional cointegration," Journal of Econometrics, Elsevier, vol. 140(2), pages 450-484, October.
    11. Wang, Bin & Wang, Man & Chan, Ngai Hang, 2015. "Residual-based test for fractional cointegration," Economics Letters, Elsevier, vol. 126(C), pages 43-46.
    12. Hualde Javier & Iacone Fabrizio, 2012. "First Stage Estimation of Fractional Cointegration," Journal of Time Series Econometrics, De Gruyter, vol. 4(1), pages 1-32, May.
    13. Shimotsu, Katsumi, 2012. "Exact local Whittle estimation of fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 169(2), pages 266-278.
    14. Guglielmo Caporale & Luis Gil-Alana, 2014. "Fractional integration and cointegration in US financial time series data," Empirical Economics, Springer, vol. 47(4), pages 1389-1410, December.
    15. Canarella, Giorgio & Miller, Stephen M., 2017. "Inflation targeting and inflation persistence: New evidence from fractional integration and cointegration," Journal of Economics and Business, Elsevier, vol. 92(C), pages 45-62.
    16. Marcel Aloy & Gilles Truchis, 2016. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems and the Co-persistence Analysis of Stock Market Realized Volatilities," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 83-104, June.
    17. da Silva, Afonso Gonçalves & Robinson, Peter M., 2008. "Fractional Cointegration In Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1207-1253, October.
    18. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.
    19. Stefanos Kechagias & Vladas Pipiras, 2015. "Definitions And Representations Of Multivariate Long-Range Dependent Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 1-25, January.
    20. Gilles de Truchis & Elena Ivona Dumitrescu, 2019. "Narrow-band Weighted Nonlinear Least Squares Estimation of Unbalanced Cointegration Systems," EconomiX Working Papers 2019-14, University of Paris Nanterre, EconomiX.

    More about this item

    Keywords

    Fractional Cointegration; Long Memory; Tapering; Periodogram;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:0412007. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.