Advertisement

Allgemeines Statistisches Archiv

, Volume 90, Issue 3, pp 439–456 | Cite as

Phillips-Perron-type unit root tests in the nonlinear ESTAR framework

  • Christoph Rothe
  • Philipp Sibbertsen
Articles

Summary

In this paper, we propose Phillips-Perron type, semi-parametric testing procedures to distinguish a unit root process from a mean-reverting exponential smooth transition autoregressive one. The limiting nonstandard distributions are derived under very general conditions and simulation evidence shows that the tests perform better than the standard Phillips-Perron or Dickey-Fuller tests in the region of the null.

Keywords

Exponential smooth transition autoregressive model unit roots Monte Carlo simulations purchasing power parity 

JEL

C12 C32 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrews, D. W. K., Monahan, J. C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator.Econometrica 60 953–966.zbMATHMathSciNetCrossRefGoogle Scholar
  2. Andrews, D. W. K., Ploberger, W. (1994). Optimal tests when a nuisance parameter is present only under the alternative.Econometrica 62 1383–1414.zbMATHMathSciNetCrossRefGoogle Scholar
  3. Baum, C. F., Barkoulas, J. T., Caglayan, M. (2001). Nonlinear adjustment to purchasing power parity in the post-Bretton Woods era.Journal of International Money and Finance 20 379–399.CrossRefGoogle Scholar
  4. Davies, R. (1987). Hypothesis testing when a nuisance parameter is present only under the alternative.Biometrika 74 33–43.zbMATHMathSciNetCrossRefGoogle Scholar
  5. Den Haan, W., Levin, A. (1997). A practitioner’s guide to robust covariance matrix estimation. InHandbook of Statistics 15 (G. Maddala and C. Rao, eds.), 299–342. Elsevier, Amsterdam.Google Scholar
  6. Dumas, B. (1992). Dynamic equilibrium and the real exchange rate in a spatially separated world.Review of Financial Studies 5 153–180.CrossRefGoogle Scholar
  7. Hansen, B. E. (1992). Convergence to stochastic integrals for dependent heterogeneous processes.Econometric Theory 8 489–500.MathSciNetGoogle Scholar
  8. Hansen, B. E. (1996). Inference when a nuisance parameter is not identified under the null hypothesis.Econometrica 64 413–430.zbMATHMathSciNetCrossRefGoogle Scholar
  9. Kapetanios, G., Shin, Y. andSnell, A. (2003). Testing for a unit root in the nonlinear star framework.Journal of Econometrics 112 359–379.zbMATHMathSciNetCrossRefGoogle Scholar
  10. Luukkonen, R., Saikkonen, P., Teräsvirta, T. (1988). Testing linearity against smooth transition autoregressive models.Biometrika 75 491–499.zbMATHMathSciNetCrossRefGoogle Scholar
  11. McLeish, D. L. (1975). A maximal inequality and dependent strong laws.Annals of Probability 3 829–839.zbMATHMathSciNetGoogle Scholar
  12. Michael, P., Nobay, A. R., Peel, D. A. (1997). Transactions costs and nonlinear adjustment in real exchange rates: An empirical investigation.Journal of Political Economy 105 862–879.CrossRefGoogle Scholar
  13. Perron, P. andNg, S. (1996). Useful modifications to some unit root tests with dependent errors and their local asymptotic properties.Review of Economic Studies 63 435–463.zbMATHCrossRefGoogle Scholar
  14. Phillips, P. C. B. (1987). Time series regression with a unit root.Econometrica 55 277–301.zbMATHMathSciNetCrossRefGoogle Scholar
  15. Phillips, P. C. B., Perron, P. (1988). Testing for a unit root in time series regression.Biometrika 75 335–346.zbMATHMathSciNetCrossRefGoogle Scholar
  16. Phillips, P. C. B., Xiao, Z. (1998). A primer on unit root testing.Journal of Economic Surveys 12 423–469.CrossRefGoogle Scholar
  17. Said, S., Dickey, D. (1984). Testing for unit roots in autoregressive moving average of unknown order.Biometrika 71 559–607.MathSciNetCrossRefGoogle Scholar
  18. Sarno, L. (2000). Real exchange rate behavior in the middle east: A reexamination.Economics Letters 66, 127–136.zbMATHCrossRefGoogle Scholar
  19. Sercu, P., Uppal, R., van Hulle, C. (1995). The exchange rate in the presence of transaction costs: Implications for tests of purchasing power parity.Journal of Finance 50 1309–1319.CrossRefGoogle Scholar
  20. Taylor, M. P., Peel, D., Sarno, L. (2001). Nonlinear mean-reversion in real exchange rates: Towards a solution to the purchasing power parity puzzles.International Economic Review 42 1015–1042.CrossRefGoogle Scholar
  21. van Dijk, D., Teräsvirta, T., Franses, P. H. (2002). Smooth transition autoregressive models—A survey of recent developments.Econometric Reviews 21 1–47.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Physica-Verlag 2006

Authors and Affiliations

  • Christoph Rothe
    • 1
  • Philipp Sibbertsen
    • 2
  1. 1.Institute of Statistics Department of EconomicsUniversity of MannheimMannheim
  2. 2.Institute of Statistics Faculty of EconomicsUniversity of HannoverHannover

Personalised recommendations