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Optimal Fractional Dickey-Fuller tests

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  • Ignacio N. Lobato
  • Carlos Velasco

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. Copyright Royal Economic Society 2006

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Bibliographic Info

Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 9 (2006)
Issue (Month): 3 (November)
Pages: 492-510

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Handle: RePEc:ect:emjrnl:v:9:y:2006:i:3:p:492-510

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Cited by:
  1. Davidson, James & Monticini, Andrea, 2010. "Tests for cointegration with structural breaks based on subsamples," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 54(11), pages 2498-2511, November.
  2. Lobato, Ignacio N. & Velasco, Carlos, 2008. "Power comparison among tests for fractional unit roots," Economics Letters, Elsevier, vol. 99(1), pages 152-154, April.
  3. Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, School of Economics and Management, University of Aarhus.
  4. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2003. "Testing for a Unit Root Against Fractional Alternatives in the Presence of a Maintained Trend," Working Papers 29, Barcelona Graduate School of Economics.
  5. Juan Jose Dolado & Jesus Gonzalo & Laura Mayoral, 2008. "Simple Wald tests of the fractional integration parameter : an overview of new results," Economics Working Papers we20080129, Universidad Carlos III, Departamento de Economía.
  6. Giuseppe Cavaliere & Morten Ørregaard Nielsen & A.M. Robert Taylor, 2013. "Bootstrap Score Tests for Fractional Integration in Heteroskedastic ARFIMA Models, with an Application to Price Dynamics in Commodity Spot and Futures Markets," Working Papers, Queen's University, Department of Economics 1309, Queen's University, Department of Economics.
  7. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus.

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