DISTRIBUTION-FREE TESTS OF FRACTIONAL COINTEGRATION

Javier Hualde and Carlos Velasco ()

Econometric Theory, 2008, vol. 24, issue 01, pages 216-255

Abstract: We 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.

Date: 2008

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Working Paper: Distribution-free Tests of Fractional Cointegration
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