IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/15292.html
   My bibliography  Save this paper

Low-Frequency Robust Cointegration Testing

Author

Listed:
  • Ulrich Müller
  • Mark W. Watson

Abstract

Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1) model for the common stochastic trends, which may not accurately describe the data's persistence. This paper discusses efficient low-frequency inference about cointegrating vectors that is robust to this potential misspecification. A simple test motivated by the analysis in Wright (2000) is developed and shown to be approximately optimal in the case of a single cointegrating vector.

Suggested Citation

  • Ulrich Müller & Mark W. Watson, 2009. "Low-Frequency Robust Cointegration Testing," NBER Working Papers 15292, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:15292
    Note: TWP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w15292.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
    2. Ulrich K. Müller, 2011. "Efficient Tests Under a Weak Convergence Assumption," Econometrica, Econometric Society, vol. 79(2), pages 395-435, March.
    3. Caner, M. & Kilian, L., 2001. "Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 639-657, October.
    4. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    5. Olivier Blanchard & Lawrence F. Katz, 1997. "What We Know and Do Not Know about the Natural Rate of Unemployment," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 51-72, Winter.
    6. Granger, Clive W J, 1993. "What Are We Learning about the Long-Run?," Economic Journal, Royal Economic Society, vol. 103(417), pages 307-317, March.
    7. Saikkonen, Pentti & Luukkonen, Ritva, 1993. "Point Optimal Tests for Testing the Order of Differencing in ARIMA Models," Econometric Theory, Cambridge University Press, vol. 9(3), pages 343-362, June.
    8. Muller, Ulrich K., 2007. "A theory of robust long-run variance estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1331-1352, December.
    9. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    10. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    11. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    12. L. R. Klein & R. F. Kosobud, 1961. "Some Econometrics of Growth: Great Ratios of Economics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(2), pages 173-198.
    13. Flint Brayton & John M. Roberts & John C. Williams, 1999. "What's happened to the Phillips curve?," Finance and Economics Discussion Series 1999-49, Board of Governors of the Federal Reserve System (U.S.).
    14. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    15. 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.
    16. Elliott, Graham & Stock, James H., 1994. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 672-700, August.
    17. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    18. 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.
    19. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, vol. 68(3), pages 695-714, May.
    20. Sriananthakumar, Sivagowry & King, Maxwell L., 2006. "A new approximate point optimal test of a composite null hypothesis," Journal of Econometrics, Elsevier, vol. 130(1), pages 101-122, January.
    21. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    22. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, September.
    23. 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.
    24. Muller, Ulrich K., 2005. "Size and power of tests of stationarity in highly autocorrelated time series," Journal of Econometrics, Elsevier, vol. 128(2), pages 195-213, October.
    25. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    26. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    27. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
    28. Hall, S G, 1986. "An Application of the Granger & Engle Two-Step Estimation Procedure to United Kingdom Aggregate Wage Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 229-239, August.
    29. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1131-1147, October.
    30. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
    31. Paul Gomme & Peter Rupert, 2004. "Measuring labors share of income," Policy Discussion Papers, Federal Reserve Bank of Cleveland, issue Nov.
    32. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November.
    33. Andrews, Donald W.K. & Moreira, Marcelo J. & Stock, James H., 2008. "Efficient two-sided nonsimilar invariant tests in IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 146(2), pages 241-254, October.
    34. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(2), pages 176-199, April.
    35. 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.
    36. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, January.
    37. 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.
    38. Robert J. Gordon, 1985. "Understanding Inflation in the 1980s," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 16(1), pages 263-302.
    39. Wright, Jonathan H, 2000. "Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 211-222, April.
    40. Yash P. Mehra, 2000. "Wage-price dynamics : are they consistent with cost push?," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 27-43.
    41. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    42. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
    43. Jansson, Michael, 2004. "Stationarity Testing With Covariates," Econometric Theory, Cambridge University Press, vol. 20(1), pages 56-94, February.
    44. Robert J. Gordon, 1998. "Foundations of the Goldilocks Economy: Supply Shocks and the Time-Varying NAIRU," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 29(2), pages 297-346.
    45. Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(5), pages 692-745, October.
    46. 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.
    47. 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.
    48. 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.
    49. 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.
    50. 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. Castelnuovo, Efrem, 2010. "Tracking U.S. inflation expectations with domestic and global indicators," Journal of International Money and Finance, Elsevier, vol. 29(7), pages 1340-1356, November.
    2. James A. Duffy & Jerome R. Simons, 2020. "Cointegration without Unit Roots," Papers 2002.08092, arXiv.org, revised Apr 2023.
    3. Pelgrin, Florian & Venditti, Alain, 2022. "On the long-run fluctuations of inheritance in two-sector OLG models," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    4. Michael D. Bauer & Glenn D. Rudebusch, 2020. "Interest Rates under Falling Stars," American Economic Review, American Economic Association, vol. 110(5), pages 1316-1354, May.
    5. Jungbin Hwang & Gonzalo Valdés, 2020. "Low Frequency Cointegrating Regression in the Presence of Local to Unity Regressors and Unknown Form of Serial Dependence," Working papers 2020-03, University of Connecticut, Department of Economics, revised Aug 2020.
    6. Hwang, Jungbin & Sun, Yixiao, 2018. "SIMPLE, ROBUST, AND ACCURATE F AND t TESTS IN COINTEGRATED SYSTEMS," Econometric Theory, Cambridge University Press, vol. 34(5), pages 949-984, October.
    7. Zhang, Rongmao & Chan, Ngai Hang, 2018. "Portmanteau-type tests for unit-root and cointegration," Journal of Econometrics, Elsevier, vol. 207(2), pages 307-324.
    8. Osabuohien-Irabor Osarumwense & Julian I. Mbegbu, 2017. "Power and Size analysis of Co-integration tests in Conditional Heteroskedascity: A Monte Carlo Simulation," Romanian Statistical Review, Romanian Statistical Review, vol. 65(3), pages 17-34, September.
    9. Moreira, Humberto Ataíde & Moreira, Marcelo J., 2013. "Contributions to the Theory of Optimal Tests," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 747, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    10. Khalaf, Lynda & Urga, Giovanni, 2014. "Identification robust inference in cointegrating regressions," Journal of Econometrics, Elsevier, vol. 182(2), pages 385-396.

    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. Andersen, Torben G. & Varneskov, Rasmus T., 2021. "Consistent inference for predictive regressions in persistent economic systems," Journal of Econometrics, Elsevier, vol. 224(1), pages 215-244.
    2. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    3. Ulrich K. Müller & Mark W. Watson, 2020. "Low-Frequency Analysis of Economic Time Series," Working Papers 2020-13, Princeton University. Economics Department..
    4. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 263-298.
    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. Jungbin Hwang & Gonzalo Valdés, 2020. "Low Frequency Cointegrating Regression in the Presence of Local to Unity Regressors and Unknown Form of Serial Dependence," Working papers 2020-03, University of Connecticut, Department of Economics, revised Aug 2020.
    7. 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.
    8. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    9. Erik Hjalmarsson & Pär Österholm, 2007. "A residual-based cointegration test for near unit root variables," International Finance Discussion Papers 907, Board of Governors of the Federal Reserve System (U.S.).
    10. Erik Hjalmarsson & Pär Österholm, 2010. "Testing for cointegration using the Johansen methodology when variables are near-integrated: size distortions and partial remedies," Empirical Economics, Springer, vol. 39(1), pages 51-76, August.
    11. 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.
    12. Maynard, Alex & Shimotsu, Katsumi, 2009. "Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence," Econometric Theory, Cambridge University Press, vol. 25(1), pages 63-116, February.
    13. Vicente Esteve, 2004. "Política fiscal y productividad del trabajo en la economía española: un análisis de series temporales," Revista de Analisis Economico – Economic Analysis Review, Universidad Alberto Hurtado/School of Economics and Business, vol. 19(1), pages 3-29, June.
    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. Elliott, Graham, 2011. "A control function approach for testing the usefulness of trending variables in forecast models and linear regression," Journal of Econometrics, Elsevier, vol. 164(1), pages 79-91, September.
    16. Nikitas Pittis & Christina Christou & Sarantis Kalyvitis & Christis Hassapis, 2009. "Long‐Run PPP under the Presence of Near‐to‐Unit Roots: The Case of the British Pound–US Dollar Rate," Review of International Economics, Wiley Blackwell, vol. 17(1), pages 144-155, February.
    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. Bunzel, Helle, 2006. "FIXED-b ASYMPTOTICS IN SINGLE-EQUATION COINTEGRATION MODELS WITH ENDOGENOUS REGRESSORS," Econometric Theory, Cambridge University Press, vol. 22(4), pages 743-755, August.
    19. Haug, Alfred A., 1996. "Tests for cointegration a Monte Carlo comparison," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 89-115.
    20. Jiang, Xiaoquan & Lee, Bong-Soo, 2007. "Stock returns, dividend yield, and book-to-market ratio," Journal of Banking & Finance, Elsevier, vol. 31(2), pages 455-475, February.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

    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:nbr:nberwo:15292. 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://edirc.repec.org/data/nberrus.html .

    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.