Consistent Testing of Cointegrating Relationships
AbstractIn 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.
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Bibliographic InfoArticle provided by Econometric Society in its journal Econometrica.
Volume (Year): 72 (2004)
Issue (Month): 6 (November)
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- 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.
- Lasak, Katarzyna, 2010.
"Likelihood based testing for no fractional cointegration,"
Journal of Econometrics,
Elsevier, vol. 158(1), pages 67-77, September.
- Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, 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).
- Katsumi Shimotsu & Morten Ørregaard Nielsen, 2006.
"Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach,"
1029, Queen's University, Department of Economics.
- 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.
- 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.
- 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.
- Javier Hualde, 2005.
Faculty Working Papers
06/05, School of Economics and Business Administration, University of Navarra.
- Avarucci, Marco & Velasco, Carlos, 2008.
"A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems,"
049, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- 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.
- Hurvich, Cliiford & Wang, Yi, 2006.
"A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects,"
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.
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