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Testing the unit root hypothesis against the logistic smooth transition autoregressive model


  • Eklund, Bruno

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


In this paper two simple tests to distinguish between unit root processes and stationary nonlinear processes are proposed. New limit distribution results are provided, together with two F type test statistics for the joint unit root and linearity hypothesis against a specific nonlinear alternative. Nonlinearity is defined through the smooth transition autoregressive model. Due to occasional size distortion in small samples, a simple bootstrap method is proposed for estimating the p-values of the tests. Power simulations show that the two proposed tests have at least the same or higher power than the corresponding Dickey-Fuller tests. Finally, as an example, the tests are applied on the seasonally adjusted U.S. monthly unemployment rate. The linear unit root hypothesis is strongly rejected, showing considerable evidence that the series is better described by a stationary smooth transition autoregressive process than a random walk.

Suggested Citation

  • Eklund, Bruno, 2003. "Testing the unit root hypothesis against the logistic smooth transition autoregressive model," SSE/EFI Working Paper Series in Economics and Finance 546, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0546

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    References listed on IDEAS

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    Cited by:

    1. He, Changli & Sandberg, Rickard, 2005. "Dickey-Fuller Type of Tests against Nonlinear Dynamic Models," SSE/EFI Working Paper Series in Economics and Finance 580, Stockholm School of Economics.
    2. Eklund, Bruno, 2003. "A nonlinear alternative to the unit root hypothesis," SSE/EFI Working Paper Series in Economics and Finance 547, Stockholm School of Economics.
    3. Joseph V. Balagtas & Matthew T. Holt, 2009. "The Commodity Terms of Trade, Unit Roots, and Nonlinear Alternatives: A Smooth Transition Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(1), pages 87-105.
    4. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94 Edward Elgar Publishing.
    5. Abderrahim Chibi & Sidi Mohamed Chekouri & Mohamed Benbouziane, 2015. "Assessing Fiscal Sustainability in Algeria: a Nonlinear Approach," Working Papers 962, Economic Research Forum, revised Oct 2015.
    6. Li, Yushu & Shukur, Ghazi, 2009. "Testing for Unit Root against LSTAR model – wavelet improvements under GARCH distortion," Working Paper Series in Economics and Institutions of Innovation 184, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    7. Craig, Lee A. & Holt, Matthew T., 2008. "Mechanical refrigeration, seasonality, and the hog-corn cycle in the United States: 1870-1940," Explorations in Economic History, Elsevier, vol. 45(1), pages 30-50, January.
    8. Holt, Matthew T. & Craig, Lee A., 2006. "AJAE Appendix: Nonlinear Dynamics and Structural Change in the U.S. Hog-Corn Ratio: A Time-Varying Star Approach," American Journal of Agricultural Economics Appendices, Agricultural and Applied Economics Association, vol. 88(1), February.

    More about this item


    Smooth transition autoregressive model; nonlinearity; unit root; Brownian motion; critical values; bootstrap; Monte Carlo simulations; unemployment rate;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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