Abstract
This paper proposes a new unit root test against a nonlinear exponential smooth transition autoregressive model. This model receives much attention in international macroeconomics as it has been successfully applied to a variety of financial time series. The new test is build upon the nonstandard testing approach of Abadir and Distaso (J Econom 140:695–718, 2007) who introduce a class of modified statistics for testing joint hypotheses when one of the alternatives is one-sided. The asymptotic properties of the suggested unit root test are derived. In a Monte Carlo study the popular Dickey–Fuller-type test proposed by Kapetanios et al. (J Econom 112:359–379, 2003) is compared to the new test. The results suggest that the new test is generally superior in terms of power. An application to a real effective exchange rate underlines its usefulness.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abadir KM, Distaso W (2007) Testing joint hypotheses when one of the alternatives is one-sided. J Econom 140: 695–718
Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74: 427–431
Dumas B (1992) Dynamic equilibrium and the real exchange rate in a spatially separated World. Rev Financial Stud 5: 153–180
Hamilton JD (1994) Time series analysis. Princeton University Press, Princetion
Hansen BE (1992) Convergence to stochastic integrals for dependent heterogeneous processes. Econom Theory 8: 489–500
Kapetanios G, Shin Y, Snell A (2003) Testing for a unit root in the nonlinear STAR framework. J Econom 112: 359–379
Luukkonen R, Saikkonen P, Teräsvirta T (1988) Testing linearity against smooth transition autoregressive models. Biometrika 75: 491–499
Michael P, Nobay AR, Peel DA (1997) Transactions costs and nonlinear adjustment in real exchange rates: an empirical investigation. J Political Econ 105: 862–879
Phillips PCB, Perron P (1988) Testing for a unit root in time series regression. Biometrika 75: 335–346
Phillips PCB, Sul D (2003) Dynamic panel estimation and homogeneity testing under cross section dependence. Econom J 6: 217–259
Rapach DE, Wohar ME (2006) The out-of-sample forecasting performance of nonlinear models of real exchange rate behavior. Int J Forecast 22: 341–361
Rothe C, Sibbertsen P (2006) Phillips-Perron-type unit root tests in the nonlinear ESTAR framework. Allgemeines Stat Arch 90: 439–456
Sandberg R (2009) Convergence to stochastic power integrals for dependent heterogeneous processes. Econom Theory (forthcoming)
Sarantis N (1999) Modeling non-linearities in real effective exchange rates. J Int Money Finance 18: 27–45
Sercu P, Uppal R, Van Hulle C (1995) The exchange rate in the presence of transaction costs: implications for tests of purchasing power parity. J Finance 50: 1309–1319
Taylor MP, Peel DA, Sarno L (2001) Nonlinear mean-reversion in real exchange rates: toward a solution to the purchasing power parity puzzles. Int Econ Rev 42: 1015–1042
Teräsvirta T (1994) Specification, estimation and evaluation of smooth transition autoregressive models. J Am Stat Assoc 89: 208–218
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kruse, R. A new unit root test against ESTAR based on a class of modified statistics. Stat Papers 52, 71–85 (2011). https://doi.org/10.1007/s00362-009-0204-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-009-0204-1