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Threshold unit root models

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Author Info

  • González, M.
  • Gonzalo, Jesús

Abstract

One of the main criticisms of unit root models is based on the theoretical fact that economic variables measured in rates cannot have unit roots. Nevertheless, standard unit root tests do not reject the existence of unit roots in many of those variables. In this paper we present a class of threshold models capable of replicating the behavior of economic variables such as unemployment, inflation and interest rates. Depending on the values of a threshold variable these models can have either a unit root or a stable root. However, despite the presence of the unit root, we prove they are stationary and geometrically ergodic. Least squares estimates of the parameters of these models are shown to be consistent and asymptotically normal. We propose the supremum of a e test in order to test the null of no threshold against the alternative of threshold when the threshold value is unknown. The limiting distribution is derived under the null of I (0) as well as under the null of 1(1). Critical values for both asymptotic distributions are computed and a finite sample study of the performance (size and power) of the tests developed in this paper is made. The paper concludes with an application to interest rates.

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Bibliographic Info

Paper provided by Universidad Carlos III de Madrid in its series Open Access publications from Universidad Carlos III de Madrid with number info:hdl:10016/6214.

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Handle: RePEc:ner:carlos:info:hdl:10016/6214

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Web page: http://www.uc3m.es

Related research

Keywords: Brownian motion; Brownian sheet; geometric ergodicity; hypothesis testing; threshold models; unit root processes;

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Cited by:
  1. Gonzalo, Jesús & Pitarakis, Jean-Yves, . "Threshold Effects in Multivariate Error Correction Models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/3220, Universidad Carlos III de Madrid.
  2. Ming Chien Lo & Eric Zivot, 1999. "Threshold Cointegration and Nonlinear Adjustment to the Law of One Price," Discussion Papers in Economics at the University of Washington 0030, Department of Economics at the University of Washington.
  3. Dipak Ghosh & Swarna (Bashu) Dutt, . "Nonstationarity and Nonlinearity in the US Unemployment Rate: A Re-examination," Journal for Economic Educators, Middle Tennessee State University, Business and Economic Research Center.
  4. Zisimos Koustas & Jean-Francois Lamarche, 2006. "Policy-Induced Mean Reversion in the Real Interest Rate?," Working Papers 0601, Brock University, Department of Economics.
  5. Baum, Anja & Koester, Gerrit B., 2011. "The impact of fiscal policy on economic activity over the business cycle - evidence from a threshold VAR analysis," Discussion Paper Series 1: Economic Studies 2011,03, Deutsche Bundesbank, Research Centre.
  6. Caner,M. & Hansen,B.E., 1998. "Threshold autoregression with a near unit root," Working papers 27, Wisconsin Madison - Social Systems.
  7. Jaya Krishnakumar & David Neto, 2009. "Testing Uncovered Interest Rate Parity and Term Structure using Three-Regime Threshold Unit Root VECM," Research Papers by the Department of Economics, University of Geneva 2009.06, Département des Sciences Économiques, Université de Genève.
  8. George Kapetanios & Yongcheol Shin, 2004. "Unit Root Tests in Three-Regime SETAR Models," ESE Discussion Papers 104, Edinburgh School of Economics, University of Edinburgh.
  9. Bec, Frederique & Guay, Alain & Guerre, Emmanuel, 2008. "Adaptive consistent unit-root tests based on autoregressive threshold model," Journal of Econometrics, Elsevier, vol. 142(1), pages 94-133, January.
  10. Martínez Ibáñez, Oscar & Olmo, José, 2008. "A nonlinear threshold model for the dependence of extremes of stationary sequences," Working Papers 2072/5361, Universitat Rovira i Virgili, Department of Economics.
  11. Gospodinov, Nikolay, 2008. "Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root," Journal of Econometrics, Elsevier, vol. 146(1), pages 146-161, September.
  12. R.P. Berben & D. van Dijk, 1999. "Unit roots and asymetric adjustment - a reassessment," Econometric Institute Report 101, Erasmus University Rotterdam, Econometric Institute.
  13. Andy Snell & George Kapetanios & Yongcheol Shin, 2004. "Testing for nonlinear cointegration between stock prices and dividends," Money Macro and Finance (MMF) Research Group Conference 2003 90, Money Macro and Finance Research Group.

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