IDEAS home Printed from https://ideas.repec.org/p/cep/stiecm/449.html
   My bibliography  Save this paper

Cointegration in Fractional Systems with Unkown Integration Orders

Author

Listed:
  • Javier Hualde
  • Peter M Robinson

Abstract

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate, and the original untapered one. For the tapered estimate, our higher-order correction involves two terms, one of order 1/vm (where m is the bandwidth number in the estimation), the other a bias term, which increases in m; depending on the relative magnitude of the terms, one or the other may dominate, or they may balance. For the untapered estimate we obtain an expansion in which, for m increasing fast enough, the correction consists only of a bias term. We discuss applications of our expansions to improved statistical inference and bandwidth choice. We assume Gaussianity, but in other respects our assumptions seem mild.

Suggested Citation

  • 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.
    • Handle: RePEc:cep:stiecm:449
    as

    Download full text from publisher

    File URL: https://sticerd.lse.ac.uk/dps/em/em449.pdf
    Download Restriction: no
    ---><---

    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. 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.
    3. Kim, Yoonbai, 1990. "Purchasing Power Parity in the Long Run: A Cointegration Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 22(4), pages 491-503, November.
    4. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    5. 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.
    6. Enders, Walter, 1988. "ARIMA and Cointegration Tests of PPP under Fixed and Flexible Exchange Rate Regimes," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 504-508, August.
    7. Robinson, P. M., 1978. "Alternative models for stationary stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 8(2), pages 141-152, December.
    8. Kim, Yoonbai, 1990. "Purchasing power parity : Another look at the long-run data," Economics Letters, Elsevier, vol. 32(4), pages 339-344, April.
    9. Corbae, Dean & Ouliaris, Sam, 1988. "Cointegration and Tests of Purchasing Power Parity," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 508-511, August.
    10. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    11. 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.
    12. 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.
    13. Saikkonen, Pentti, 1995. "Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 11(5), pages 888-911, October.
    14. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Working Papers 9617, Banco de España.
    15. Robinson, Peter M. & Velasco, Carlos, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics 2273, London School of Economics and Political Science, LSE Library.
    16. Peter M Robinson & Carlos Velasco, 2000. "Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series - (Now published in Journal of the American Statistical Association, 95, (2000), pp.1229-1243.)," STICERD - Econometrics Paper Series 391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    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. Hualde, Javier & Robinson, Peter M., 2003. "Cointegration in fractional systems with unkown integration orders," LSE Research Online Documents on Economics 58050, London School of Economics and Political Science, LSE Library.
    2. 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.
    3. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 263-298.
    4. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    5. 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.
    6. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-879, August.
    7. 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.
    8. Javier Hualde & Peter M Robinson, 2006. "Semiparametric Estimation of Fractional Cointegration," STICERD - Econometrics Paper Series 502, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Mallory Mindy & Lence Sergio H., 2012. "Testing for Cointegration in the Presence of Moving Average Errors," Journal of Time Series Econometrics, De Gruyter, vol. 4(2), pages 1-68, November.
    10. Luis Gil-Alana, 2004. "The permanent income hypothesis: A new framework based on fractional integration and cointegration," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 10(3), pages 165-179, October.
    11. Hualde, Javier, 2006. "Unbalanced Cointegration," Econometric Theory, Cambridge University Press, vol. 22(5), pages 765-814, October.
    12. Froot, Kenneth A. & Rogoff, Kenneth, 1995. "Perspectives on PPP and long-run real exchange rates," Handbook of International Economics, in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 32, pages 1647-1688, Elsevier.
    13. Peter M Robinson, 2004. "The Distance between Rival Nonstationary Fractional Processes," STICERD - Econometrics Paper Series 468, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    15. Hualde, Javier & Robinson, Peter M., 2006. "Semiparametric Estimation of Fractional Cointegration," LSE Research Online Documents on Economics 4537, London School of Economics and Political Science, LSE Library.
    16. Wang, Chong, 1998. "Testing for purchasing power parity: a nonlinear approach," ISU General Staff Papers 1998010108000013534, Iowa State University, Department of Economics.
    17. 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.
    18. Okimoto, Tatsuyoshi & Shimotsu, Katsumi, 2010. "Decline in the persistence of real exchange rates, but not sufficient for purchasing power parity," Journal of the Japanese and International Economies, Elsevier, vol. 24(3), pages 395-411, September.
    19. 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.
    20. Luis A. Gil‐Alana, 2003. "Testing of Fractional Cointegration in Macroeconomic Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(4), pages 517-529, September.

    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:cep:stiecm:449. 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: the person in charge (email available below). General contact details of provider: https://sticerd.lse.ac.uk/_new/publications/ .

    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.