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Testing for a Unit Root against Transitional Autoregressive Models

  • Joon Y. Park
  • Mototsugu Shintani

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.

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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 321307000000000316.

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Date of creation: 02 Sep 2006
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Handle: RePEc:cla:levrem:321307000000000316
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  1. Frédérique Bec & Mélika Bensalem & Marine Carrasco, 2010. "Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime STAR Model," Post-Print hal-00685810, HAL.
  2. Frédérique Bec & Alain Guay & Emmanuel Guerre, 2002. "Adaptive Consistent Unit Root Tests Based on Autoregressive Threshold Model," Working Papers 2002-46, Centre de Recherche en Economie et Statistique.
  3. George Kapetanios & Yongcheol Shin, 2002. "Unit Root Tests in Three-Regime SETAR Models," Working Papers 465, Queen Mary University of London, School of Economics and Finance.
  4. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
  5. Olivier J. Blanchard & Lawrence H. Summers, 1986. "Hysteresis and the European Unemployment Problem," Working papers 427, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
  7. Maurice Obstfeld & Alan M. Taylor, 1997. "Nonlinear Aspects of Goods-Market Arbitrage and Adjustment: Heckscher's Commodity Points Revisited," NBER Working Papers 6053, National Bureau of Economic Research, Inc.
  8. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
  9. Philip Rothman, . "Forecasting Asymmetric Unemployment Rates," Working Papers 9618, East Carolina University, Department of Economics.
  10. Alan M. Taylor, 2000. "Potential Pitfalls for the Purchasing-Power-Parity Puzzle? Sampling and Specification Biases in Mean-Reversion Tests of the Law of One Price," NBER Working Papers 7577, National Bureau of Economic Research, Inc.
  11. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
  12. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-45, August.
  13. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  14. Taylor, Mark P & Peel, David A & Sarno, Lucio, 2001. "Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution to the Purchasing Power Parity Puzzles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1015-42, November.
  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.
  16. n/a, 2001. "Balance of payments prospects in EMU," NIESR Discussion Papers 164, National Institute of Economic and Social Research.
  17. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-79, August.
  18. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
  19. Frederic Bec & Melika Ben Salem & Marine Carrasco, 2004. "Tests for Unit-Root versus Threshold Specification With an Application to the Purchasing Power Parity Relationship," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 382-395, October.
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