IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v29y2008i6p1088-1103.html
   My bibliography  Save this article

Fractional cointegration in the presence of linear trends

Author

Listed:
  • Uwe Hassler
  • Francesc Marmol
  • Carlos Velasco

Abstract

. We consider bivariate regressions of nonstationary fractionally integrated variables dominated by linear time trends. The asymptotic behaviour of the ordinary least square (OLS) estimators in this case allows limiting normality to arise at a faster rate of convergence than if the individual series were detrended, increasing in this way the power of the tests for fractional cointegration. We also show that the limiting distribution of the t‐ratio of the slope coefficient depends upon the presence or not of a deterministic trend in the conditional regressor. We introduce the concept of local fractional trend to explain the apparently diverging asymptotic theories that apply when a trend is either present or absent in our set‐up.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:6:p:1088-1103
    DOI: 10.1111/j.1467-9892.2008.00597.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2008.00597.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2008.00597.x?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
    ---><---

    References listed on IDEAS

    as
    1. Ingolf Dittmann, 2001. "Fractional cointegration of voting and non-voting shares," Applied Financial Economics, Taylor & Francis Journals, vol. 11(3), pages 321-332.
    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. Breitung, Jorg & Hassler, Uwe, 2002. "Inference on the cointegration rank in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 167-185, October.
    4. 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.
    5. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    6. D. Marinucci, 2000. "Spectral Regression For Cointegrated Time Series With Long‐Memory Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(6), pages 685-705, November.
    7. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
    8. 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.
    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. Abul M.M. Masih & Rumi Masih, 1998. "A Fractional Cointegration Approach to Testing Mean Reversion Between Spot and Forward Exchange Rates: A Case of High Frequency Data with Low Frequency Dynamics," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 25(7‐8), pages 987-1003, September.
    11. Juan J. Dolado & Francesc Marmol, 2004. "Asymptotic inference results for multivariate long-memory processes," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 168-190, June.
    12. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    13. 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.
    14. Haldrup, Niels & Hylleberg, Svend, 1995. "A note on the distribution of the least squares estimator of a random walk with drift: Some analytical evidence," Economics Letters, Elsevier, vol. 48(3-4), pages 221-228, June.
    15. Tsay, Wen-Jen, 2000. "Estimating Trending Variables In The Presence Of Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 16(3), pages 324-346, June.
    16. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
    17. 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.
    18. 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.
    19. Abul M.M. Masih & Rumi Masih, 1998. "A Fractional Cointegration Approach to Testing Mean Reversion Between Spot and Forward Exchange Rates: A Case of High Frequency Data with Low Frequency Dynamics," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 25(7‐8), pages 987-1003, September.
    20. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
    21. 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.
    22. Phillips, P.C.B., 1988. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations," Econometric Theory, Cambridge University Press, vol. 4(3), pages 528-533, December.
    23. Abdol Soofi, 1998. "A fractional cointegration test of purchasing power parity: the case of selected members of OPEC," Applied Financial Economics, Taylor & Francis Journals, vol. 8(6), pages 559-566.
    24. G. Geoffrey Booth & Yiuman Tse, 1995. "Long memory in interest rate futures markets: A fractional cointegration analysis," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 15(5), pages 573-584, August.
    25. Baillie, Richard T & Bollerslev, Tim, 1994. "Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-745, June.
    26. 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.
    27. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
    28. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
    29. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, vol. 72(6), pages 1809-1844, November.
    30. 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.
    31. Nabeya, Seiji & Sørensen, Bent E., 1994. "Asymptotic Distributions of the Least-Squares Estimators and Test Statistics in the Near Unit Root Model with Non-Zero Initial Value and Local Drift and Trend," Econometric Theory, Cambridge University Press, vol. 10(5), pages 937-966, December.
    Full references (including those not matched with items on IDEAS)

    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. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    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. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    4. Wang, Bin & Wang, Man & Chan, Ngai Hang, 2015. "Residual-based test for fractional cointegration," Economics Letters, Elsevier, vol. 126(C), pages 43-46.
    5. 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.
    6. 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.
    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. Breitung, Jorg & Hassler, Uwe, 2002. "Inference on the cointegration rank in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 167-185, October.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Hualde, Javier, 2006. "Unbalanced Cointegration," Econometric Theory, Cambridge University Press, vol. 22(5), pages 765-814, October.
    15. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.
    16. 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.
    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. Margherita Gerolimetto & Isabella Procidano, 2008. "A test for fractional cointegration using the sieve bootstrap," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 373-391, 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. Gerolimetto, Margherita, 2006. "Frequency domain bootstrap for the fractional cointegration regression," Economics Letters, Elsevier, vol. 91(3), pages 389-394, June.

    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:bla:jtsera:v:29:y:2008:i:6:p:1088-1103. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.