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A nonlinear alternative to the unit root hypothesis

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  • Eklund, Bruno

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

Abstract

This paper considers testing the unit root hypothesis against a smooth transition autoregressive model as the alternative. The model specification makes it possible to discriminate between nonstationary random walk and stationary nonlinear processes. Some new limit results are presented, extending earlier work, and two F type tests are proposed. Small sample simulations show some size distortions, why a bootstrap method for estimating p-values to the tests are considered. Power simulations show some gain in power, compared to the common Augmented Dickey-Fuller tests. Finally, the two proposed F type tests are applied on a number of real exchange rates. For several of the exchange rates considered the linear unit root is rejected in favor of the stationary nonlinear model, supporting the purchasing power parity hypothesis.

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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 547.

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Length: 23 pages
Date of creation: 28 Nov 2003
Date of revision:
Handle: RePEc:hhs:hastef:0547

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Related research

Keywords: Smooth transition autoregressive model; nonlinearity; unit root; Brownian motion; bootstrap; critical values; Monte Carlo simulations; real exchange rates;

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References

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  1. Bruce E. Hansen & Mehmet Caner, 1997. "Threshold Autoregressions with a Unit Root," Boston College Working Papers in Economics, Boston College Department of Economics 381, Boston College Department of Economics.
  2. 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, American Statistical Association, vol. 16(3), pages 304-11, July.
  3. 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.
  4. Ken Froot & Kenneth Rogoff, . "Perspectives on PPP and Long-Run Real Exchange Rates," Working Paper 32027, Harvard University OpenScholar.
  5. Hamori, Shigeyuki & Tokihisa, Akira, 1997. "Testing for a unit root in the presence of a variance shift1," Economics Letters, Elsevier, Elsevier, vol. 57(3), pages 245-253, December.
  6. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-80.
  7. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  8. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 8(04), pages 489-500, December.
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Citations

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Cited by:
  1. JamesR. Lothian & MarkP. Taylor, 2008. "Real Exchange Rates Over the Past Two Centuries: How Important is the Harrod-Balassa-Samuelson Effect?," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 118(532), pages 1742-1763, October.
  2. Michael Dueker & Zacharias Psaradakis & Martin Sola & Fabio Spagnolo, 2009. "Multivariate Contemporaneous Threshold Autoregressive Models," Department of Economics Working Papers, Universidad Torcuato Di Tella 2009-03, Universidad Torcuato Di Tella.
  3. I A Venetis & I Paya & D Peel, 2009. "ESTAR model with multiple fixed points. Testing and Estimation," Working Papers 599093, Lancaster University Management School, Economics Department.
  4. repec:lan:wpaper:2453 is not listed on IDEAS
  5. repec:lan:wpaper:2374 is not listed on IDEAS
  6. repec:lan:wpaper:2372 is not listed on IDEAS
  7. repec:lan:wpaper:2595 is not listed on IDEAS
  8. Craig, Lee & Holt, Matthew T., 2012. "The Role of Mechanical Refrigeration in Spatial and Temporal Price Dynamics for Regional U.S. Egg Markets, 1880–1911," MPRA Paper 39554, University Library of Munich, Germany.

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