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On the Asymptotic Distribution of the DF–GLS Test Statistic

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  • Joakim Westerlund

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    (Deakin University)

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    Abstract

    In a very influential paper Elliott et al. (Efficient Tests for an Autoregressive Unit Root, Econometrica 64, 813–836, 1996) show that no uniformly most powerful test for the unit root testing problem exits, derive the relevant power envelope and characterize a family of point-optimal tests. As a by-product, they also propose a “GLS detrended” version of the conventional Dickey–Fuller test, denoted DF–GLS, that has since then become very popular among practitioners, much more so than the point-optimal tests. In view of this, it is quite strange to find that, while conjectured in Elliott et al. (1996), so far there seems to be no formal proof of the asymptotic distribution of the DF–GLS test statistic. By providing three separate proofs the current paper not only substantiates the required result, but also provides insight regarding the pros and cons of different methods of proof.

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    File URL: http://www.deakin.edu.au/buslaw/aef/workingpapers/fin-econometrics/2014_03.pdf
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    Bibliographic Info

    Paper provided by Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance in its series Financial Econometics Series with number 2014_03.

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    Length: 25
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    Handle: RePEc:dkn:ecomet:fe_2014_03

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    Related research

    Keywords: Unit root test; GLS detrending; Asymptotic distribution; Asymptotic local power; Method of proof.;

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    1. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    2. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, 05.
    3. Michael Jansson & Morten Ørregaard Nielsen, 2009. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Working Papers 1213, Queen's University, Department of Economics.
    4. Graham Elliott & Michael Jansson, . "Testing for Unit Roots with Stationary Covariates," Economics Working Papers 2000-6, School of Economics and Management, University of Aarhus.
    5. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
    6. Smeekes Stephan, 2009. "Detrending Bootstrap Unit Root Tests," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics 300., Boston College Department of Economics.
    8. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
    9. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, 07.
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