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Semiparametric Tests for Double Unit Roots

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  • Haldrup, Niels

Abstract

In this article, I argue that if an explosive root is considered a serious alternative to an I(2) process, then joint testing for the number of unit roots along the lines of Hasza and Fuller is preferable instead of prior differencing as suggested by Dickey and Pantula. A semiparametric equivalent of the Hasza-Fuller test that permits rather general assumptions about the innovation process is developed. The test is a straightforward generalization of the Phillips Z test for a single unit root. Through Monte Carlo simulations, the different tests are compared, and the article is completed by an empirical application examining the purchasing power parity for several Latin American countries for which both explosive and double unit roots may be a possibility.

Suggested Citation

  • Haldrup, Niels, 1994. "Semiparametric Tests for Double Unit Roots," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 109-122, January.
  • Handle: RePEc:bes:jnlbes:v:12:y:1994:i:1:p:109-22
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    Citations

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    Cited by:

    1. Niels Haldrup & Peter Lildholdt, 2005. "Local power functions of tests for double unit roots," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(2), pages 159-179.
    2. Bianco, Dominique & Salies, Evens, 2009. "Productivité et R&D au Luxembourg
      [Productivity and R&D in Luxembourg]
      ," MPRA Paper 21170, University Library of Munich, Germany.
    3. Shin, Dong Wan & So, Beong Soo, 2002. "Recursive mean adjustment and tests for nonstationarities," Economics Letters, Elsevier, vol. 75(2), pages 203-208, April.
    4. Dolado, Juan J. & Marmol, Francesc, 1997. "On the properties of the Dickey-Pantula test against fractional alternatives," Economics Letters, Elsevier, vol. 57(1), pages 11-16, November.
    5. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, May.
    6. Francesco Bravo, 2010. "Nonparametric likelihood inference for general autoregressive models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(1), pages 79-106, March.
    7. Niels Haldrup & Peter Lildholdt, "undated". "On the Robustness of Unit Root Tests in the Presence of Double Unit Roots," Economics Working Papers 2000-1, Department of Economics and Business Economics, Aarhus University.
    8. Yoon, Gawon, 2005. "An introduction to I([infinity]) processes," Economic Modelling, Elsevier, vol. 22(3), pages 473-483, May.
    9. Dong Shin & Man-Suk Oh, 2003. "Tests for the order of integration against higher order integration," Statistical Papers, Springer, vol. 44(3), pages 383-396, July.
    10. Holtemöller, Oliver, 2002. "Money and prices: An I(2) analysis for the euro area," SFB 373 Discussion Papers 2002,12, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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