Unit Root Tests in Three-Regime SETAR Models
AbstractThis 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 - 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 clearly 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 bilateral real exchange rates for the G7 countries.
Download InfoIf 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.
Bibliographic InfoPaper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 104.
Date of creation: Mar 2004
Date of revision:
Self-exciting Threshold Autoregressive Models; Unit Roots; Globally Stationary Processes; Threshold Cointegration; Monte Carlo Simulations; Real Exchange Rates; Transactions Costs; Dread of Depreciation;
Other versions of this item:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-03-14 (All new papers)
- NEP-ECM-2004-03-14 (Econometrics)
- NEP-ETS-2004-03-14 (Econometric Time Series)
- NEP-IFN-2004-03-14 (International Finance)
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.:
- n/a, 2001. "Balance of payments prospects in EMU," NIESR Discussion Papers 164, National Institute of Economic and Social Research.
- 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.
- 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.
- Tom Doan, . "RATS programs to replicate Enders/Granger JBES(1998)on threshold unit roots," Statistical Software Components RTZ00054, Boston College Department of Economics.
- 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.
- 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.
- 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.
- Jayasri Dutta, 2002. "Dread of Depreciation," IMF Working Papers 02/63, International Monetary Fund.
- 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.
- 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.
- Bruce E. Hansen & Mehmet Caner, 1997.
"Threshold Autoregressions with a Unit Root,"
Boston College Working Papers in Economics
381, Boston College Department of Economics.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Nathan S. Balke & Thomas B. Fomby, 1992.
9209, Federal Reserve Bank of Dallas.
- 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.
- 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.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Gina Reddie).
If references are entirely missing, you can add them using this form.