IDEAS home Printed from https://ideas.repec.org/a/bpj/jtsmet/v4y2012i1n2.html
   My bibliography  Save this article

First Stage Estimation of Fractional Cointegration

Author

Listed:
  • Hualde Javier

    (Universidad Pública de Navarra)

  • Iacone Fabrizio

    (University of York)

Abstract

In a fractionally cointegrated model, we analyze, both theoretically and by means of a Monte Carlo experiment, the performance of the most popular first stage estimation methods, including ordinary and narrow band least squares (Robinson, 1994), difference taper narrow band least squares (Chen and Hurvich, 2003a), instrumental variables (Robinson and Gerolimetto, 2006), and compare it with the behavior of a new proposal, the integrated ordinary least squares. An appropriate version of this latter estimator (and also of the instrumental variables one) achieves in all circumstances the fastest convergence rate (among other first stage methods) and performs well in finite samples. The use of improved first stage methods is most important in cases of low collective memory of regressor and cointegrating error. This is particularly relevant in multivariate settings, where the key parameters which rule the convergence properties of the estimators are the memories of adjacent cointegrating subspaces.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:jtsmet:v:4:y:2012:i:1:n:2
    DOI: 10.1515/1941-1928.1129
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/1941-1928.1129
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/1941-1928.1129?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 263-298.
    3. D Marinucci & Peter M Robinson, 1998. "Alternative Forms of Fractional Brownian Motion - (Now published in Journal of Statistical Planning and Inference, 80 (1999), pp.111-122.)," STICERD - Econometrics Paper Series 354, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series 449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002. "Band Spectral Regression with Trending Data," Econometrica, Econometric Society, vol. 70(3), pages 1067-1109, May.
    6. 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.
    7. Morten Ørregaard Nielsen & Per Frederiksen, 2011. "Fully modified narrow‐band least squares estimation of weak fractional cointegration," Econometrics Journal, Royal Economic Society, vol. 14, pages 77-120, February.
    8. Robinson, P.M., 2005. "The distance between rival nonstationary fractional processes," Journal of Econometrics, Elsevier, vol. 128(2), pages 283-300, October.
    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. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November.
    11. 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.
    12. Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(5), pages 692-745, October.
    13. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
    14. Robinson, Peter M. & Hualde, Javier, 2003. "Cointegration in fractional systems with unknown integration orders," LSE Research Online Documents on Economics 2223, London School of Economics and Political Science, LSE Library.
    15. 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.
    16. 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.
    17. P.M. Robinson & D. Marinucci, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 149-160, January.
    18. P. M. Robinson & M. Gerolimetto, 2006. "Instrumental variables estimation of stationary and non-stationary cointegrating regressions," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 291-306, July.
    19. 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.
    20. D Marinucci & Peter M Robinson, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," STICERD - Econometrics Paper Series 408, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    21. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(4), pages 583-621, August.
    22. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
    23. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Working Papers 9617, Banco de España.
    24. 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.
    25. Marinucci, D & Robinson, Peter M., 2000. "The averaged periodogram for nonstationary vector time series," LSE Research Online Documents on Economics 2294, London School of Economics and Political Science, LSE Library.
    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. 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.
    2. Javier Hualde & Fabrizio Iacone, 2015. "Autocorrelation robust inference using the Daniell kernel with fixed bandwidth," Discussion Papers 15/14, Department of Economics, University of York.
    3. Marcel Aloy & Gilles de Truchis, 2013. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems," Working Papers halshs-00879522, HAL.
    4. Javier Hualde & Fabrizio Iacone, 2015. "Small-b and Fixed-b Asymptotics for Weighted Covariance Estimation in Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 528-540, July.

    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. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 263-298.
    2. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    3. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    4. Hualde, Javier, 2006. "Unbalanced Cointegration," Econometric Theory, Cambridge University Press, vol. 22(5), pages 765-814, October.
    5. 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.
    6. 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.
    7. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
    8. 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.
    9. Uwe Hassler & Francesc Marmol & Carlos Velasco, 2008. "Fractional cointegration in the presence of linear trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1088-1103, November.
    10. 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.
    11. Gilles de Truchis & Elena Ivona Dumitrescu & Florent Dubois, 2019. "Local Whittle Analysis of Stationary Unbalanced Fractional Cointegration Systems," EconomiX Working Papers 2019-15, University of Paris Nanterre, EconomiX.
    12. Gilles de Truchis & Florent Dubois & Elena Ivona Dumitrescu, 2019. "Local Whittle Analysis of Stationary Unbalanced Fractional Cointegration Systems," Working Papers hal-04141882, HAL.
    13. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.
    14. Müller, Ulrich K. & Watson, Mark W., 2013. "Low-frequency robust cointegration testing," Journal of Econometrics, Elsevier, vol. 174(2), pages 66-81.
    15. 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.
    16. Hualde, Javier, 2014. "Estimation of long-run parameters in unbalanced cointegration," Journal of Econometrics, Elsevier, vol. 178(2), pages 761-778.
    17. 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.
    18. P. M. Robinson & M. Gerolimetto, 2006. "Instrumental variables estimation of stationary and non-stationary cointegrating regressions," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 291-306, July.
    19. 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.
    20. Gilles de Truchis & Elena Ivona Dumitrescu, 2019. "Narrow-band Weighted Nonlinear Least Squares Estimation of Unbalanced Cointegration Systems," Working Papers hal-04141871, HAL.

    More about this item

    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:bpj:jtsmet:v:4:y:2012:i:1:n:2. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.