Unit root tests in three-regime SETAR models
This paper proposes a simple testing procedure to distinguish a unit root process from a globally stationary three-regime self-exciting threshold autoregressive process. Following the threshold cointegration literature we assume that the process follows the random walk in the corridor regime, and therefore we propose that the null of a unit root be tested by the Wald statistic for the joint significance of autoregressive parameters in both lower and upper regimes. We establish that when threshold parameters are known, the suggested Wald test has a well-defined asymptotic null distribution free of nuisance parameters. In the general case where threshold parameters are unknown a priori, we consider the three most commonly used summary statistics based on their average, exponential average and supremum. Assuming that the grid set for thresholds can be selected such that the corridor regime be of finite width both under the null and under the alternative, we can establish both stochastic equicontinuity and uniform convergence of the aforementioned summary statistics. Monte Carlo evidence indicates that the proposed tests are more powerful than the Dickey--Fuller test that ignores the threshold nature under the alternative. We illustrate the usefulness of our proposed tests by examining stationarity of real exchange rates for the G7 countries. Copyright Royal Economic Society 2006
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 9 (2006)
Issue (Month): 2 (07)
|Contact details of provider:|| Postal: |
Phone: +44 1334 462479
Web page: http://www.res.org.uk/
More information through EDIRC
|Order Information:||Web: http://www.ectj.org|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Tweedie, Richard L., 1975. "Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space," Stochastic Processes and their Applications, Elsevier, vol. 3(4), pages 385-403, October.
- 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.
- Anderson, Heather M, 1997. "Transaction Costs and Non-linear Adjustment towards Equilibrium in the US Treasury Bill Market," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(4), pages 465-84, November.
- 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 304-11, July.
- Enders, Walter & Granger, C. W. J., 1998. "Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Staff General Research Papers 1388, Iowa State University, Department of Economics.
- Nathan S. Balke & Thomas B. Fomby, 1992.
9209, Federal Reserve Bank of Dallas.
- Frédérique Bec & Alain Guay & Emmanuel Guerre, 2002.
"Adaptive Consistent Unit Root Tests Based on Autoregressive Threshold Model,"
2002-46, Centre de Recherche en Economie et Statistique.
- 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.
- Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
- Pippenger, Michael K & Goering, Gregory E, 1993. "A Note on the Empirical Power of Unit Root Tests under Threshold Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(4), pages 473-81, November.
- Jayasri Dutta, 2002. "Dread of Depreciation: Measuring Real Exchange Rate Interventions," IMF Working Papers 02/63, International Monetary Fund.
- George Kapetanios & Yongcheol Shin & Andy Snell, 2003. "Testing for Cointegration in Nonlinear STAR Error Correction Models," Working Papers 497, Queen Mary University of London, School of Economics and Finance.
- Bruce E. Hansen & Mehmet Caner, 1997.
"Threshold Autoregressions with a Unit Root,"
Boston College Working Papers in Economics
381, Boston College Department of Economics.
- Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
- Shin, Dong Wan & Lee, Oesook, 2001. "Tests for Asymmetry in Possibly Nonstationary Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 233-44, April.
- 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.
- Dirk Te Velde, 2001. "Balance of payments prospects in EMU," NIESR Discussion Papers 178, National Institute of Economic and Social Research.
- Christos Ioannidis & David A. Peel & Michael J. Peel, 2003. "The Time Series Properties of Financial Ratios: Lev Revisited," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(5-6), pages 699-714.
- Lo, Ming Chien & Zivot, Eric, 2001. "Threshold Cointegration And Nonlinear Adjustment To The Law Of One Price," Macroeconomic Dynamics, Cambridge University Press, vol. 5(04), pages 533-576, September.
- 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.
- Tom Doan, . "RATS programs to replicate Michael-Nobay-Peel ESTAR models," Statistical Software Components RTZ00113, Boston College Department of Economics.
When requesting a correction, please mention this item's handle: RePEc:ect:emjrnl:v:9:y:2006:i:2:p:252-278. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)or (Christopher F. Baum)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.