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Local Power Functions of Tests for Double Unit Roots

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  • Niels Haldrup
  • Peter Lildholdt

    ()
    (Department of Economics, University of Aarhus, Denmark)

Abstract

The purpose of this paper is to characterize three commonly used double unit root tests in terms of their asymptotic local power. To this end, we study a class of nearly doubly integrated processes which in the limit will behave as a weighted integral of a double indexed Ornstein-Uhlenbeck process. Based on a numerical examination of the analytical distributions, a comparison of the tests is made via their asymptotic local power functions.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2000-2.

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Length: 32
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Handle: RePEc:aah:aarhec:2000-2

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Web page: http://www.econ.au.dk/afn/

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Keywords: Asymptotic local power function; Brownian motion; Ornstein-Uhlenbeck process;

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References

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  1. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  2. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1991. "Stochastic trends and economic fluctuations," Working Paper Series, Macroeconomic Issues 91-4, Federal Reserve Bank of Chicago.
  3. Haldrup, Niels, 1994. "Semiparametric Tests for Double Unit Roots," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 109-22, January.
  4. Haldrup, Niels, 1994. "The asymptotics of single-equation cointegration regressions with I(1) and I(2) variables," Journal of Econometrics, Elsevier, vol. 63(1), pages 153-181, July.
  5. Nabeya, Seiji & Perron, Pierre, 1994. "Local asymptotic distribution related to the AR(1) model with dependent errors," Journal of Econometrics, Elsevier, vol. 62(2), pages 229-264, June.
  6. Shin, Dong Wan & Kim, Hyun Jung, 1999. "Semiparametric Tests for Double Unit Roots Based on Symmetric Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 67-73, January.
  7. Choi, In & Park, Joon Y. & Yu, Byungchul, 1997. "Canonical Cointegrating Regression and Testing for Cointegration in the Presence of I(1) and I(2) Variables," Econometric Theory, Cambridge University Press, vol. 13(06), pages 850-876, December.
  8. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche 9427, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  9. Perron, P. & Ng, S., 1996. "An Autoregressive Spectral Density Estimator at Frequency Zero for Nonstationarity Tests," Cahiers de recherche 9611, Universite de Montreal, Departement de sciences economiques.
  10. Jeganathan, P., 1991. "On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 7(03), pages 269-306, September.
  11. Sen, D L & Dickey, David A, 1987. "Symmetric Test for Second Differencing in Univariate Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 463-73, October.
  12. Swensen, Anders Rygh, 1993. "A Note on Asymptotic Power Calculations in Nearly Nonstationary Time Series," Econometric Theory, Cambridge University Press, vol. 9(04), pages 659-667, August.
  13. Dickey, David A & Pantula, Sastry G, 1987. "Determining the Ordering of Differencing in Autoregressive Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 455-61, October.
  14. Niels Haldrup, 1998. "An Econometric Analysis of I(2) Variables," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 595-650, December.
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Citations

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Cited by:
  1. Nikolaj Malchow-Moeller & Bo Jellesmark Thorsen, . "A Dynamic Agricultural Household Model with Uncertain Income and Irreversible and Indivisible Investments under Credit Constraints," Economics Working Papers 2000-7, School of Economics and Management, University of Aarhus.
  2. Boriss Siliverstovs, . "The Bi-parameter Smooth Transition AutoRegressive model," Economics Working Papers 2000-16, School of Economics and Management, University of Aarhus.
  3. Effrosyni Diamantoudi, . "Equilibrium Binding Agreements under Diverse Bahavioral Assumptions," Economics Working Papers 2001-9, School of Economics and Management, University of Aarhus.
  4. Nikolaj Malchow-Moeller & Bo Jellesmark Thorsen, . "Investment under Uncertainty - the Case of Repeated Investment Options," Economics Working Papers 2000-15, School of Economics and Management, University of Aarhus.
  5. Anton Skrobotov, 2013. "Double Unit Roots Testing, GLS-detrending and Uncertainty over the Initial Conditions," Working Papers 0083, Gaidar Institute for Economic Policy, revised 2013.
  6. Bo Sandemann Rasmussen, . "Government Debt and Capital Accumulation in the Blanchard-Cass-Yaari OLG Model," Economics Working Papers 2000-14, School of Economics and Management, University of Aarhus.

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