Consistent Testing of Cointegrating Relationships
Abstract
In this paper we investigate methods for testing the existence of a cointegration relationship among the components of a nonstationary fractionally integrated (NFI) vector time series. Our framework generalizes previous studies restricted to unit root integrated processes and permits simultaneous analysis of spurious and cointegrated NFI vectors. We propose a modified F-statistic, based on a particular studentization, which converges weakly under both hypotheses, despite the fact that OLS estimates are only consistent under cointegration. This statistic leads to a Wald-type test of cointegration when combined with a narrow band GLS-type estimate. Our semiparametric methodology allows consistent testing of the spurious regression hypothesis against the alternative of fractional cointegration without prior knowledge on the memory of the original series, their short run properties, the cointegrating vector, or the degree of cointegration. This semiparametric aspect of the modelization does not lead to an asymptotic loss of power, permitting the Wald statistic to diverge faster under the alternative of cointegration than when testing for a hypothesized cointegration vector. In our simulations we show that the method has comparable power to customary procedures under the unit root cointegration setup, and maintains good properties in a general framework where other methods may fail. We illustrate our method testing the cointegration hypothesis of nominal GNP and simple-sum (M1, M2, M3) monetary aggregates. Copyright The Econometric Society 2004.Download Info
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic Info
Article provided by Econometric Society in its journal Econometrica.
Volume (Year): 72 (2004)
Issue (Month): 6 (November)
Pages: 1809-1844
Contact details of provider:
Phone: 1 212 998 3820
Fax: 1 212 995 4487
Email:
Web page: http://www.econometricsociety.org/
More information through EDIRC
Order Information:
Email:
Web: http://www.blackwellpublishing.com/memb.asp?ref=0012-9682
Related research
Keywords:Other versions of this item:
- Francesc, Marmol & Velasco, Carlos, . "Consistent testing of cointegrating relationships," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4415, Universidad Carlos III de Madrid.
References
References listed on IDEASPlease report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gonzalo, Jesús & Lee, Tae-Hwy, .
"Pitfalls in testing for long run relationships,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/753, Universidad Carlos III de Madrid.
- Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
- Gonzalo, J. & Lee, T.H., 1995. "Pitfalls in Testing for Long Run Relationships," Papers 38, Boston University - Department of Economics.
- Clive Granger & Namwon Hyung & Yongil Jeon, 2001.
"Spurious regressions with stationary series,"
Applied Economics,
Taylor and Francis Journals, vol. 33(7), pages 899-904.
- Granger, Clive W.J. & Hyung, Namwon & Jeon, Yongil, 1998. "Spurious Regressions with Stationary Series," University of California at San Diego, Economics Working Paper Series qt7r3353t8, Department of Economics, UC San Diego.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Phillips, P.C.B., 1986.
"Understanding spurious regressions in econometrics,"
Journal of Econometrics,
Elsevier, vol. 33(3), pages 311-340, December.
- Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
- Granger, E.J. & Swanson, N.R., 1996.
"An introduction to stochastic Unit Root Processes,"
Papers
4-96-3, Pennsylvania State - Department of Economics.
- Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
- Marmol, Francesc & Velasco, Carlos, .
"Trend stationarity versus long-range dependence in time series analysis,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/4349, Universidad Carlos III de Madrid.
- Marmol, Francesc & Velasco, Carlos, 2002. "Trend stationarity versus long-range dependence in time series analysis," Journal of Econometrics, Elsevier, vol. 108(1), pages 25-42, May.
- Hassler, U. & Marmol, Francesc & Velasco, Carlos, .
"Residual log-periodogram inference for long-run relationships,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/4359, Universidad Carlos III de Madrid.
- 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.
- Hassler, Uwe & Marmol, Francesc & Velasco, Carlos, 2002. "Residual log-periodogram inference for long-run relationships," Publications of Darmstadt Technical University, Institute of Economics (VWL) 18289, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).
- Hassler, Uwe & Marmol, Francesc & Velasco, Carlos, 2002. "Residual Log-Periodogram Inference for Long-Run-Relationships," Publications of Darmstadt Technical University, Institute of Economics (VWL) 37317, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).
- Hassler, Uwe & Marmol, Francesc & Velasco, Carlos, 2002. "Residual Log-Periodogram Inference for Long-Run-Relationships," Darmstadt Discussion Papers in Economics 37317, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).
- Hassler, Uwe & Marmol, Francesc & Velasco, Carlos, . "Residual Log-Periodogram Inference for Long-Run-Relationships," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4431, Universidad Carlos III de Madrid.
- Robinson, Peter M. & Yajima, Yoshihiro, 2002.
"Determination of cointegrating rank in fractional systems,"
Journal of Econometrics,
Elsevier, vol. 106(2), pages 217-241, February.
- Peter M Robinson & Yoshihiro Yajima, 2001. "Determination of Cointegrating Rank in Fractional Systems," STICERD - Econometrics Paper Series /2001/423, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Tsay, Wen-Jen & Chung, Ching-Fan, 2000. "The spurious regression of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 155-182, May.
- Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
- 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 103-12, January.
- Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
- Peter C.B. Phillips & Sam Ouliaris, 1987.
"Asymptotic Properties of Residual Based Tests for Cointegration,"
Cowles Foundation Discussion Papers
847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
- Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
- Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
- Robinson, P.M. & Velasco, Carlos, . "Autocorrelation-Robust Inference," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4529, Universidad Carlos III de Madrid.
- Andrews, Donald W K, 1991.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Econometrica,
Econometric Society, vol. 59(3), pages 817-58, May.
- Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Kramer, Walter & Marmol, Francesc, 2004. "The power of residual-based tests for cointegration when residuals are fractionally integrated," Economics Letters, Elsevier, vol. 82(1), pages 63-69, January.
- Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
- Abdol Soofi, 1998. "A fractional cointegration test of purchasing power parity: the case of selected members of OPEC," Applied Financial Economics, Taylor and Francis Journals, vol. 8(6), pages 559-566.
- Baillie, R.T. & Bollerslev, T., 1993.
"Cointegration, Fractional Cointegration, and Exchange RAte Dynamics,"
Papers
9103, Michigan State - Econometrics and Economic Theory.
- Baillie, Richard T & Bollerslev, Tim, 1994. " Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-45, June.
- Jansson, Michael & Haldrup, Niels, 2002. "Regression Theory For Nearly Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1309-1335, December.
- Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
- Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
- Haldrup, Niels, 1994. "The asymptotics of single-equation cointegration regressions with I(1) and I(2) variables," Journal of Econometrics, Elsevier, vol. 63(1), pages 153-181, July.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Esther Stroe-Kunold & Joachim Werner, 2009. "A drunk and her dog: a spurious relation? Cointegration tests as instruments to detect spurious correlations between integrated time series," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(6), pages 913-940, November.
- 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.
- Katsumi Shimotsu & Morten Ørregaard Nielsen, 2006. "Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach," Working Papers 1029, Queen's University, Department of Economics.
- Katarzyna Lasak, 2008.
"Likelihood based testing for no fractional cointegration,"
CREATES Research Papers
2008-52, School of Economics and Management, University of Aarhus.
- Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
- Javier Hualde, 2005.
"Unbalanced Cointegration,"
Faculty Working Papers
06/05, School of Economics and Business Administration, University of Navarra.
- Hualde, Javier, 2006. "Unbalanced Cointegration," Econometric Theory, Cambridge University Press, vol. 22(05), pages 765-814, October.
- Javier Hualde & Peter M Robinson, 2006.
"Root-N-Consistent Estimation Of Weakfractional Cointegration,"
STICERD - Econometrics Paper Series
/2006/499, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- 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.
- Javier Hualde & A Robinson, 2006. "Root-N-Consistent Estimation Of Weakfractional Cointegration," STICERD - Econometrics Paper Series /06/499, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- 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.
- Hurvich, Clifford & Wang, Yi, 2009. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects," MPRA Paper 12575, University Library of Munich, Germany.
- Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus.
- Mauro Costantini & Roy Cerqueti, 2007. "Non parametric Fractional Cointegration Analysis," ISAE Working Papers 78, ISTAT - Italian National Institute of Statistics - (Rome, ITALY).
- Avarucci, Marco & Velasco, Carlos, 2008.
"A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems,"
Research Memoranda
049, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- 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.
Lists
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.Statistics
Access and download statisticsCorrections
When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:72:y:2004:i:6:p:1809-1844For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.

