Premium
Efficient Wald Tests for Fractional Unit Roots
Author(s) -
Lobato Ignacio N,
Velasco Carlos
Publication year - 2007
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/j.1468-0262.2006.00758.x
Subject(s) - wald test , unit root , mathematics , score test , lagrange multiplier , multiplier (economics) , null hypothesis , nonlinear system , unit root test , square root , simple (philosophy) , mathematical optimization , statistics , statistical hypothesis testing , economics , physics , cointegration , quantum mechanics , macroeconomics , geometry , philosophy , epistemology
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.