Distribution-Free Tests Of Fractional Cointegration
AbstractWe propose tests of the null of spurious relationship against the alternative of fractional cointegration among the components of a vector of fractionally integrated time series. Our test statistics have an asymptotic chi-square distribution under the null and rely on generalized least squares type of corrections that control for the short-run correlation of the weak dependent components of the fractionally integrated processes. We emphasize corrections based on nonparametric modelization of the innovations autocorrelation, relaxing important conditions that are standard in the literature and, in particular, being able to consider simultaneously (asymptotically) stationary or nonstationary processes. Relatively weak conditions on the corresponding short-run and memory parameter estimates are assumed. The new tests are consistent with a divergence rate that, in most of the cases, as we show in a simple situation, depends on the cointegration degree. Finite-sample properties of the tests are analyzed by means of a Monte Carlo experiment.We thank Helmut L tkepohl and two referees for helpful comments and suggestions. We also thank participants at the NSF NBER Time Series Conference at the University of Heidelberg, Germany, at the Unit Root and Cointegration Testing Conference at the University of Algarve, Faro, Portugal, and seminar participants at the Universidad de Navarra and Ente Luigi Einaudi for helpful comments. Javier Hualde s research is supported by the Spanish Ministerio de Educaci n y Ciencia through Juan de la Cierva and Ram n y Cajal contracts and ref. SEJ2005-07657 ECON. Carlos Velasco s research is supported by the Spanish Ministerio de Educaci n y Ciencia, ref. SEJ2004-04583 ECON.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 24 (2008)
Issue (Month): 01 (February)
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Other versions of this item:
- Javier Hualde & Carlos Velasco, . "Distribution-free Tests of Fractional Cointegration," Faculty Working Papers 08/06, School of Economics and Business Administration, University of Navarra.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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- 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.
- Avarucci, Marco & Velasco, Carlos, 2008. "A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems," Research Memorandum 049, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- 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, 2012. "Estimation of the cointegrating rank in fractional cointegration," Documentos de Trabajo - Lan Gaiak Departamento de EconomÃa - Universidad PÃºblica de Navarra 1205, Departamento de Economía - Universidad Pública de Navarra.
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