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Dickey-Fuller Type of Tests against Nonlinear Dynamic Models

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Author Info
He, Changli () (Dept. of Economic Statistics, Stockholm School of Economics)
Sandberg, Rickard () (Dept. of Economic Statistics, Stockholm School of Economics)
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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Publisher 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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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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  1. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
    Other versions:
  2. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
    Other versions:
  4. David I. Harvey & Terence C. Mills, 2002. "Unit roots and double smooth transitions," Journal of Applied Statistics, Taylor and Francis Journals, vol. 29(5), pages 675-683, July. [Downloadable!] (restricted)
  5. Saikkonen, Pentti & L tkepohl, Helmut, 2002. "Testing For A Unit Root In A Time Series With A Level Shift At Unknown Time," Econometric Theory, Cambridge University Press, vol. 18(02), pages 313-348, April. [Downloadable!]
  6. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November. [Downloadable!] (restricted)
    Other versions:
  7. 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 880, Cowles Foundation, Yale University. [Downloadable!]
  8. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
    Other versions:
  9. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
    Other versions:
  10. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-20, July.
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  11. Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-11, July.
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  12. M. Lanne & H. Lütkepohl, . "Unit Root Tests for Time Series with Level Shifts: A Comparison of Different Proposals," Sonderforschungsbereich 373 2001-5, Humboldt Universitaet Berlin.
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  13. Eklund, Bruno, 2003. "Testing the unit root hypothesis against the logistic smooth transition autoregressive model," Working Paper Series in Economics and Finance 546, Stockholm School of Economics. [Downloadable!]
  14. 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, vol. 10(3), pages 271-87, July.
  15. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February. [Downloadable!] (restricted)
  16. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June. [Downloadable!] (restricted)
    Other versions:
  17. 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, vol. 65(1), pages 91-115, February. [Downloadable!] (restricted)
    Other versions:
  18. He, Changli & Sandberg, Rickard, 2005. "Testing Parameter Constancy in Unit Root Autoregressive Models Against Continuous Change," Working Paper Series in Economics and Finance 579, Stockholm School of Economics, revised 08 Feb 2005. [Downloadable!]
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