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Dickey-Fuller Type of Tests against Nonlinear Dynamic Models

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  • He, Changli

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Sandberg, Rickard

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

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    Abstract

    In this paper we introduce several test statistics of testing the null hypotheses of a random walk (with or without drift) against models that accommodate a smooth nonlinear shift in the level, the dynamic structure, and the trend. We derive analytical limiting distributions for all tests. Finite sample properties are examined. The performance of the tests is compared to that of the classical unit root tests by Dickey-Fuller and Phillips and Perron, and is found to be superior in terms of power.

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    File URL: http://swopec.hhs.se/hastef/papers/hastef0580.pdf
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    Bibliographic Info

    Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 580.

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    Length: 37 pages
    Date of creation: 23 Jan 2005
    Date of revision:
    Handle: RePEc:hhs:hastef:0580

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    Related research

    Keywords: Dickey-Fuller test; LSTAR(p); LSTART(p); Nonlinear trends; Parameter constancy; Unit root; Brownian motion;

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    References

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    1. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers, Princeton, Department of Economics - Econometric Research Program 338, Princeton, Department of Economics - Econometric Research Program.
    2. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 932, Cowles Foundation for Research in Economics, Yale University.
    3. Helmut Luetkepohl & Pentti Saikkonen, 2000. "Testing for a Unit Root in a Time Series with a Level Shift at Unknown Time," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 0342, Econometric Society.
    4. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0073, National Bureau of Economic Research, Inc.
    5. Vogelsang, T.I. & Perron, P., 1991. "Nonstationary and Level Shifts With An Application To Purchasing Power Parity," Papers, Princeton, Department of Economics - Econometric Research Program 359, Princeton, Department of Economics - Econometric Research Program.
    6. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 10(3), pages 271-87, July.
    7. Enders, Walter & Granger, C. W. J., 1998. "Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Staff General Research Papers, Iowa State University, Department of Economics 1388, Iowa State University, Department of Economics.
    8. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
    9. Markku Lanne & Helmut Lutkepohl & Pentti Saikkonen, 2003. "Test Procedures for Unit Roots in Time Series with Level Shifts at Unknown Time," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, Department of Economics, University of Oxford, vol. 65(1), pages 91-115, February.
    10. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
    11. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, Elsevier, vol. 62(2), pages 211-228, June.
    12. Peter C.B. Phillips & Sam Ouliaris & Joon Y. Park, 1988. "Testing for a Unit Root in the Presence of a Maintained Trend," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 880, Cowles Foundation for Research in Economics, Yale University.
    13. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 944, Cowles Foundation for Research in Economics, Yale University.
    14. David Harvey & Terence Mills, 2002. "Unit roots and double smooth transitions," Journal of Applied Statistics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 29(5), pages 675-683.
    15. n/a, 2001. "Balance of payments prospects in EMU," NIESR Discussion Papers, National Institute of Economic and Social Research 164, National Institute of Economic and Social Research.
    16. Eklund, Bruno, 2003. "Testing the unit root hypothesis against the logistic smooth transition autoregressive model," Working Paper Series in Economics and Finance, Stockholm School of Economics 546, Stockholm School of Economics.
    17. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, Elsevier, vol. 112(2), pages 359-379, February.
    18. He, Changli & Sandberg, Rickard, 2005. "Testing Parameter Constancy in Unit Root Autoregressive Models Against Continuous Change," Working Paper Series in Economics and Finance, Stockholm School of Economics 579, Stockholm School of Economics, revised 08 Feb 2005.
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