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Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime star Model

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  • Frédérique Bec
  • Mélika Ben Salem
  • Marine Carrasco

Abstract

Recent studies on general equilibrium models with transaction costs show that the dynamics of the real exchange rate are necessarily nonlinear. Our contribution to the literature on nonlinear price adjustment mechanisms is threefold. First, we model the real exchange rate by a Multi-Regime Logistic Smooth Transition Auto Regression (MR-LSTAR), allowing for both ESTAR-type and SETAR-type dynamics. This choice is motivated by the fact that even the theoretical models, which predict a smooth behavior for the real exchange rate, do not rule out the possibility of a discontinuous adjustment as a limit case. Second, we propose two classes of unit-root tests against this MR-LSTAR alternative, based respectively on the likelihood and on an auxiliary model. Their asymptotic distributions are derived analytically. Third, when applied to 28 bilateral real exchange rates, our tests reject the null hypothesis of a unit root for eleven series bringing evidence in favor of the purchasing power parity.

Suggested Citation

  • Frédérique Bec & Mélika Ben Salem & Marine Carrasco, 2010. "Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime star Model," Annals of Economics and Statistics, GENES, issue 99-100, pages 395-427.
  • Handle: RePEc:adr:anecst:y:2010:i:99-100:p:395-427
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    Cited by:

    1. Peter Martey Addo & Monica Billio & Dominique Guegan, 2011. "A New Modelling Test: The Univariate MT-STAR Model," Documents de travail du Centre d'Economie de la Sorbonne 11083r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Aug 2013.
    2. Grossmann, Axel & McMillan, David G., 2010. "Forecasting exchange rates: Non-linear adjustment and time-varying equilibrium," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 20(4), pages 436-450, October.
    3. Stephen Norman, 2009. "Testing for a unit root against ESTAR nonlinearity with a delay parameter greater than one," Economics Bulletin, AccessEcon, vol. 29(3), pages 2152-2173.
    4. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    5. 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.
    6. 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.
    7. Nicolau João, 2011. "Purchasing Power Parity Analyzed from a Continuous-Time Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(3), pages 1-26, May.
    8. 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.
    9. Addo, Peter Martey & Billio, Monica & Guégan, Dominique, 2014. "The univariate MT-STAR model and a new linearity and unit root test procedure," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 4-19.
    10. Lo, Ming Chien & Morley, James, 2015. "Bayesian analysis of nonlinear exchange rate dynamics and the purchasing power parity persistence puzzle," Journal of International Money and Finance, Elsevier, vol. 51(C), pages 285-302.
    11. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    12. Zhang, Lingxiang, 2013. "Modeling China's inflation dynamics: An MRSTAR approach," Economic Modelling, Elsevier, vol. 31(C), pages 440-446.
    13. 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.
    14. Cerrato, Mario & Kim, Hyunsok & MacDonald, Ronald, 2009. "Technical Appendix-3-Regime asymmetric STAR modeling and exchange rate reversion," SIRE Discussion Papers 2009-37, Scottish Institute for Research in Economics (SIRE).
    15. Joon Y. Park & Mototsugu Shintani, 2016. "Testing For A Unit Root Against Transitional Autoregressive Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 635-664, May.
    16. Daiki Maki & Shin-ichi Kitasaka, 2015. "Residual-based tests for cointegration with three-regime TAR adjustment," Empirical Economics, Springer, vol. 48(3), pages 1013-1054, May.
    17. McMillan, David G., 2009. "The confusing time-series behaviour of real exchange rates: Are asymmetries important?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(4), pages 692-711, October.
    18. Shintani, Mototsugu & Terada-Hagiwara, Akiko & Yabu, Tomoyoshi, 2013. "Exchange rate pass-through and inflation: A nonlinear time series analysis," Journal of International Money and Finance, Elsevier, vol. 32(C), pages 512-527.
    19. Cho, Dooyeon & Doblas-Madrid, Antonio, 2014. "Trade intensity and purchasing power parity," Journal of International Economics, Elsevier, vol. 93(1), pages 194-209.
    20. Kim, Bong-Han & Min, Hong-Ghi & Moh, Young-Kyu, 2010. "Nonlinear dynamics in exchange rate deviations from the monetary fundamentals: An empirical study," Economic Modelling, Elsevier, vol. 27(5), pages 1167-1177, September.
    21. Peter Martey Addo & Monica Billio & Dominique Guegan, 2011. "A test for a new modelling: The Univariate MT-STAR Model," Documents de travail du Centre d'Economie de la Sorbonne 11083, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    22. Enders, Walter & Pascalau, Razvan, 2015. "Pretesting for multi-step-ahead exchange rate forecasts with STAR models," International Journal of Forecasting, Elsevier, vol. 31(2), pages 473-487.
    23. Mauro Ferreira, 2011. "Capturing asymmetry in real exchange rate with quantile autoregression," Applied Economics, Taylor & Francis Journals, vol. 43(3), pages 327-340.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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