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Testing for a Unit Root against Transitional Autoregressive Models

Author

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  • Joon Y. Park

    (Department of Economics, Rice University and SKKU)

  • Mototsugu Shintani

    () (Department of Economics, Vanderbilt University)

Abstract

This paper considers the test of a unit root in transitional autoregressive models. In particular, we develop the asymptotic theory of the inf-t test for the null hypothesis of a unit root in a wide class of nonlinear autoregressive models having parameters that are identified only under the alternative of stationarity. Our framework is very general and allows for virtually all potentially interesting models with the threshold, discrete and smooth transition functions. The specifications of shortrun dynamics used in the paper are also fully general, and comparable to those used in the linear unit root models. Most importantly, our asymptotics take it into consideration that the parameter space has a random limit. This is an essential feature of the unit root test in transitional autoregressive models, which has been ignored in the literature. For this very general class of transitional autoregressive models, we show that the inf-t test has well-defined limit distribution depending only upon the transition function and the limit parameter space. The critical values of the test are provided for some of the commonly used models under the conventional specification of the parameter space. Our simulation study shows that the test has good size with the power that is significantly higher than the usual ADF test even for samples of relatively small sizes. We apply the test to various economic time series and find strong evidence for the rejection of random walks in favor of stationary transitional autoregressive models.

Suggested Citation

  • Joon Y. Park & Mototsugu Shintani, 2005. "Testing for a Unit Root against Transitional Autoregressive Models," Vanderbilt University Department of Economics Working Papers 05010, Vanderbilt University Department of Economics.
  • Handle: RePEc:van:wpaper:0510
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    2. Le Pen, Yannick, 2011. "A pair-wise approach to output convergence between European regions," Economic Modelling, Elsevier, vol. 28(3), pages 955-964, May.
    3. Tsangyao Chang & Yu-Shao Liu & Chi-Wei Su, 2012. "Purchasing power parity with nonlinear and asymmetric smooth adjustment for the Middle Eastern countries," Applied Economics Letters, Taylor & Francis Journals, vol. 19(5), pages 487-491, March.
    4. Doo-Yull Choi & Bong-Han Kim & See-Won Kim, 2011. "Nonlinear mean-reversion in Southeast Asian real exchange rates," Applied Financial Economics, Taylor & Francis Journals, vol. 21(19), pages 1409-1421.
    5. George Kapetanios & Yongcheol Shin, 2011. "Testing the Null Hypothesis of Nonstationary Long Memory Against the Alternative Hypothesis of a Nonlinear Ergodic Model," Econometric Reviews, Taylor & Francis Journals, vol. 30(6), pages 620-645.
    6. Kim, Hyeongwoo & Ryu, Deockhyun, 2015. "A nonparametric study of real exchange rate persistence over a century," International Review of Economics & Finance, Elsevier, vol. 37(C), pages 406-418.
    7. Tsangyao Chang & Hsu-Ling Chang & Ken Hung & Chi-Wei Su, 2012. "Nonlinear adjustment to purchasing power parity for Germany's real exchange rate relative to its major trading partners," Applied Economics Letters, Taylor & Francis Journals, vol. 19(2), pages 197-202, February.
    8. Kim, Hyeongwoo & Moh, Young-Kyu, 2010. "A century of purchasing power parity confirmed: The role of nonlinearity," Journal of International Money and Finance, Elsevier, vol. 29(7), pages 1398-1405, November.
    9. Bec, Frédérique & Zeng, Songlin, 2013. "Are Southeast Asian real exchange rates mean reverting?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 23(C), pages 265-282.
    10. 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.
    11. Stephen Norman & Kerk Phillips, 2013. "What is the shape of real exchange rate nonlinearity?," Applied Financial Economics, Taylor & Francis Journals, vol. 23(5), pages 363-375, March.
    12. Silva Lopes, Artur C. & Florin Zsurkis, Gabriel, 2017. "Are linear models really unuseful to describe business cycle data?," MPRA Paper 79413, University Library of Munich, Germany.
    13. Maki Daiki, 2010. "Detection of Stationarity in Nonlinear Processes: A Comparison between Structural Breaks and Three-Regime TAR Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-43, September.
    14. Joanna Bruzda, 2008. "Output-Capital Nexus in the Solow and Romer Growth Models. LSTR or ESTR Cointegration?," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 8, pages 103-110.
    15. repec:bok:journl:v:18:y:2012:i:4:p:1-22 is not listed on IDEAS
    16. Rehim Kılıc, 2011. "Testing for a unit root in a stationary ESTAR process," Econometric Reviews, Taylor & Francis Journals, vol. 30(3), pages 274-302.
    17. Lopes, Artur Silva & Zsurkis, Gabriel Florin, 2017. "Are linear models really unuseful to describe business cycle data?," Economics Discussion Papers 2017-5, Kiel Institute for the World Economy (IfW).
    18. Tsangyao Chang & Chi-Wei Su & Chia-Hao Lee, 2012. "Nonlinear adjustment to purchasing power parity with flexible Fourier function in G-7 countries," Applied Economics Letters, Taylor & Francis Journals, vol. 19(12), pages 1111-1116, August.
    19. Mario Cerrato & Hyunsok Kim & Ronald Macdonald, 2010. "Three-Regime Asymmetric STAR Modeling and Exchange Rate Reversion," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(7), pages 1447-1467, October.
    20. Mario Cerrato & Hyunsok Kim & Ronald MacDonald, 2008. "3-Regime symmetric STAR modeling and exchange rate reversion," Working Papers 2009_05, Business School - Economics, University of Glasgow, revised Feb 2009.
    21. Tsangyao Chang & Chia-Hao Lee & Pei-I Chou, 2012. "Nonlinear adjustment to purchasing power parity in G-7 countries," Applied Economics Letters, Taylor & Francis Journals, vol. 19(2), pages 123-128, February.
    22. Tsangyao Chang, 2012. "Nonlinear adjustment to purchasing power parity in China," Applied Economics Letters, Taylor & Francis Journals, vol. 19(9), pages 843-848, June.
    23. Hyeongwoo Kim & Liliana Stern & Michael Stern, 2009. "Nonlinear mean reversion in the G7 stock markets," Applied Financial Economics, Taylor & Francis Journals, vol. 19(5), pages 347-355.
    24. Yoon, Gawon, 2010. "Do real exchange rates really follow threshold autoregressive or exponential smooth transition autoregressive models?," Economic Modelling, Elsevier, vol. 27(2), pages 605-612, March.

    More about this item

    Keywords

    unit root test; threshold autoregressive models (TAR); logistic and exponential smooth transition autoregressive models (LSTAR and ESTAR);

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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