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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.

Suggested Citation

  • 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.
    • Handle: RePEc:hhs:hastef:0547
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    File URL: http://swopec.hhs.se/hastef/papers/hastef0547.pdf
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    References listed on IDEAS

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    1. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
    2. 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.
    3. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
    4. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-180.
    5. Froot, Kenneth A. & Rogoff, Kenneth, 1995. "Perspectives on PPP and long-run real exchange rates," Handbook of International Economics, in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 32, pages 1647-1688, Elsevier.
    6. 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 304-311, July.
    7. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    8. Hamori, Shigeyuki & Tokihisa, Akira, 1997. "Testing for a unit root in the presence of a variance shift1," Economics Letters, Elsevier, vol. 57(3), pages 245-253, December.
    9. G. M. Grossman & K. Rogoff (ed.), 1995. "Handbook of International Economics," Handbook of International Economics, Elsevier, edition 1, volume 3, number 3.
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    Citations

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    Cited by:

    1. James R. Lothian & Mark P. Taylor, 2008. "Real Exchange Rates Over the Past Two Centuries: How Important is the Harrod‐Balassa‐Samuelson Effect?," Economic Journal, Royal Economic Society, vol. 118(532), pages 1742-1763, October.
    2. 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.
    3. Abderrahim Chibi & Sidi Mohamed Chekouri & Mohamed Benbouziane, 2019. "Debt sustainability, structural breaks and nonlinear fiscal adjustment: empirical evidence from Algeria," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 66(4), pages 369-397, December.
    4. Tm Mokoena, 2007. "Taking The Puzzle Out Of The Purchasing Power Parity Puzzle: An Application In Respect Of South Africa," South African Journal of Economics, Economic Society of South Africa, vol. 75(1), pages 22-34, March.
    5. repec:lan:wpaper:2453 is not listed on IDEAS
    6. repec:lan:wpaper:2374 is not listed on IDEAS
    7. 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.
    8. Dueker, Michael J. & Psaradakis, Zacharias & Sola, Martin & Spagnolo, Fabio, 2011. "Multivariate contemporaneous-threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 160(2), pages 311-325, February.
    9. Dilem Yildirim & Ralf Becker & Denise R Osborn, 2009. "Bootstrap Unit Root Tests for Nonlinear Threshold Models," Economics Discussion Paper Series 0915, Economics, The University of Manchester.
    10. Abderrahim Chibi & Sidi Mohamed Chekouri & Mohamed Benbouziane, 2019. "The dynamics of fiscal policy in Algeria: sustainability and structural change," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-27, December.
    11. repec:lan:wpaper:2372 is not listed on IDEAS
    12. repec:lan:wpaper:2595 is not listed on IDEAS

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    More about this item

    Keywords

    Smooth transition autoregressive model; nonlinearity; unit root; Brownian motion; bootstrap; critical values; Monte Carlo simulations; real exchange rates;
    All these keywords.

    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
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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