Optimal Fractional Dickey-Fuller Tests

19 Pages Posted: 1 Nov 2006

See all articles by Ignacio N. Lobato

Ignacio N. Lobato

Instituto Tecnológico Autónomo de México (ITAM) - Centro de Investigacion Economica

Carlos Velasco

Universidad Carlos III de Madrid - Department of Economics

Abstract

This article analyzes the fractional Dickey-Fuller (FDF) test for unit roots recently introduced by Dolado, Gonzalo and Mayoral (2002 Econometrica 70, 1963-2006) within a more general setup. These authors motivate their test with a particular analogy with the Dickey-Fuller test, whereas we interpret the FDF test as a class of tests indexed by an auxiliary parameter, which can be chosen to maximize the power of the test. Within this framework, we investigate optimality aspects of the FDF test and show that the version of the test proposed by these authors is not optimal. For the white noise case, we derive simple optimal FDF tests based on consistent estimators of the true degree of integration. For the serial correlation case, optimal augmented FDF (AFDF) tests are difficult to implement since they depend on the short-term component. Hence, we propose a feasible procedure that automatically optimizes a prewhitened version of the AFDF test and avoids this problem.

Suggested Citation

Lobato, Ignacio N. and Velasco, Carlos, Optimal Fractional Dickey-Fuller Tests. Econometrics Journal, Vol. 9, No. 3, pp. 492-510, November 2006. Available at SSRN: https://ssrn.com/abstract=941533 or http://dx.doi.org/10.1111/j.1368-423X.2006.00195.x

Ignacio N. Lobato (Contact Author)

Instituto Tecnológico Autónomo de México (ITAM) - Centro de Investigacion Economica ( email )

Av. Camino a Santa Teresa #930
Col. Heroes de Padierna
Mexico City, D.F. 10370
Mexico

Carlos Velasco

Universidad Carlos III de Madrid - Department of Economics ( email )

Calle Madrid 126
Getafe, 28903
Spain
+34-91 6249646 (Phone)
+34-91 6249875 (Fax)

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