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A Fractional Dickey-Fuller Test for Unit Roots


  • Juan J. Dolado

    () (Universidad Carlos III de Madrid, Spain)

  • Jesus Gonzalo

    () (Universidad Carlos III de Madrid, Spain)

  • Laura Mayoral

    () (Universitat Autonoma de Barcelona, Spain)


This paper presents a new test for fractionally integrated ("FI") processes. In particular, we propose a testing procedure in the time domain that extends the well-known Dickey-Fuller approach, originally designed for the "I"(1) versus "I"(0) case, to the more general setup of "FI"("d"-sub-0) versus "FI"("d"-sub-1), with "d"-sub-1<"d"-sub-0. When "d"-sub-0=1, the proposed test statistics are based on the OLS estimator, or its "t"-ratio, of the coefficient on Δ-super-"d"-sub-1"y"-sub-"t" - 1 in a regression of Δ"y-sub-t" on Δ-super-"d"-sub-1"y"-sub-"t" - 1 and, possibly, some lags of Δ"y-sub-t". When "d"-sub-1 is not taken to be known a priori, a pre-estimation of "d"-sub-1 is needed to implement the test. We show that the choice of any "T"-super-1/2-consistent estimator of "d"-sub-1 is an element of [0 ,1) suffices to make the test feasible, while achieving asymptotic normality. Monte-Carlo simulations support the analytical results derived in the paper and show that proposed tests fare very well, both in terms of power and size, when compared with others available in the literature. The paper ends with two empirical applications. Copyright The Econometric Society 2002.

Suggested Citation

  • Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2002. "A Fractional Dickey-Fuller Test for Unit Roots," Econometrica, Econometric Society, vol. 70(5), pages 1963-2006, September.
  • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:5:p:1963-2006

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    References listed on IDEAS

    1. Kim-Sau Chung & J.C. Ely, 2007. "Foundations of Dominant-Strategy Mechanisms," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 447-476.
    2. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
    3. Brusco, Sandro, 1998. "Unique Implementation of the Full Surplus Extraction Outcome in Auctions with Correlated Types," Journal of Economic Theory, Elsevier, vol. 80(2), pages 185-200, June.
    4. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41 World Scientific Publishing Co. Pte. Ltd..
    5. Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," Econometrica, Econometric Society, vol. 73(6), pages 1771-1813, November.
    6. d'Aspremont, C. & Gerard-Varet, L. -A., 1982. "Bayesian incentive compatible beliefs," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 83-103, June.
    7. Neeman, Zvika, 2003. "The effectiveness of English auctions," Games and Economic Behavior, Elsevier, vol. 43(2), pages 214-238, May.
    8. Robert, Jacques, 1991. "Continuity in auction design," Journal of Economic Theory, Elsevier, vol. 55(1), pages 169-179, October.
    9. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-361, March.
    10. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
    11. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    12. Jean-Jacques Laffont & David Martimort, 2000. "Mechanism Design with Collusion and Correlation," Econometrica, Econometric Society, vol. 68(2), pages 309-342, March.
    13. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
    14. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    15. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
    16. McAfee, R Preston & McMillan, John & Reny, Philip J, 1989. "Extracting the Surplus in the Common-Value Auction," Econometrica, Econometric Society, vol. 57(6), pages 1451-1459, November.
    17. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March.
    18. Johnson, Scott & Pratt, John W & Zeckhauser, Richard J, 1990. "Efficiency Despite Mutually Payoff-Relevant Private Information: The Finite Case," Econometrica, Econometric Society, vol. 58(4), pages 873-900, July.
    19. Aoyagi, Masaki, 1998. "Correlated Types and Bayesian Incentive Compatible Mechanisms with Budget Balance," Journal of Economic Theory, Elsevier, vol. 79(1), pages 142-151, March.
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