We thank a co-editor and two referees for very useful comments, J. Arteche, M. Avarucci, M. Delgado, J. Dolado, L. Gil-Alaña, J. Gonzalo, J. Hidalgo, L. Mayoral, P. Perron, W. Ploberger, and P. Robinson for useful conversations, and seminar participants at the London School of Economics and at the 2005 Econometric Society World Congress. This research was financed by the Spanish Ministerio de Educación y Ciencia (SEJ2004-04583/ECON). Part of this research was carried out while Lobato was visiting Universidad Carlos III de Madrid thanks to the Spanish Secretaría de Estado de Universidades e Investigación (SAB2004-0034). Lobato acknowledges financial support from Asociación Mexicana de Cultura and from the Mexican Consejo Nacional de Ciencia y Tecnología (CONACYT) under project grant 41893-S.
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Efficient Wald Tests for Fractional Unit Roots
Article first published online: 28 FEB 2007
DOI: 10.1111/j.1468-0262.2006.00758.x
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How to Cite
Lobato, I. N. and Velasco, C. (2007), Efficient Wald Tests for Fractional Unit Roots. Econometrica, 75: 575–589. doi: 10.1111/j.1468-0262.2006.00758.x
Publication History
- Issue published online: 28 FEB 2007
- Article first published online: 28 FEB 2007
- Manuscript received May, 2005; final revision received October, 2006.
- Abstract
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- Cited By
Keywords:
- Long memory;
- serial correlation;
- Dickey–Fuller test;
- Lagrange multiplier test;
- fractional processes;
- local power
In this article we introduce efficient Wald tests for testing the null hypothesis of the unit root against the alternative of the fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson Lagrange multiplier tests. Our results contrast with the tests for fractional unit roots, introduced by Dolado, Gonzalo, and Mayoral, which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first-order asymptotic properties of the proposed tests are not affected by the preestimation of short or long memory parameters.