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A Test For Stationarity Versus Trends And Unit Roots For A Wide Class Of Dependent Errors

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  • Giraitis, Liudas
  • Leipus, Remigijus
  • Philippe, Anne

Abstract

We suggest a rescaled variance type of test for the null hypothesis of stationarity against deterministic and stochastic trends (unit roots). The deterministic trend can be represented as a general function in time (e.g., nonparametric, linear, or polynomial regression, abrupt changes in the mean). Under the null, the asymptotic distribution of the test is derived, and critical values are tabulated for a wide class of stationary processes with short, long, or negative dependence structure. A simulation study examines the performance of the test in terms of size and power. The empirical performance of the test is illustrated using the S&P 500 data.The authors thank the editor, the referees, and Karim Abadir for helpful comments and Alfredas Račkauskas for drawing our attention to the criterion of Cremers and Kadelka (1986). The first author's work was supported by the ESRC grants R000238212 and R000239538. The last two authors were supported by a cooperation agreement CNRS/LITHUANIA (4714) and by a bilateral Lithuania-France research project Gilibert.

Suggested Citation

  • Giraitis, Liudas & Leipus, Remigijus & Philippe, Anne, 2006. "A Test For Stationarity Versus Trends And Unit Roots For A Wide Class Of Dependent Errors," Econometric Theory, Cambridge University Press, vol. 22(6), pages 989-1029, December.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:06:p:989-1029_06
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    Cited by:

    1. Zhongjun Qu, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 423-438, July.
    2. Bailey, Natalia & Giraitis, Liudas, 2016. "Spectral approach to parameter-free unit root testing," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 4-16.
    3. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    4. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2010. "A two-sample test for comparison of long memory parameters," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2118-2136, October.
    5. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    6. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    7. Francis Ahking, 2010. "Non-parametric tests of real exchange rates in the post-Bretton Woods era," Empirical Economics, Springer, vol. 39(2), pages 439-456, October.
    8. Laura Mayoral, 2006. "Further Evidence on the Statistical Properties of Real GNP," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 901-920, December.
    9. Juan J. Dolado & Heiko Rachinger & Carlos Velasco, 2022. "LM Tests for Joint Breaks in the Dynamics and Level of a Long-Memory Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 629-650, April.
    10. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
    11. Bailey, Natalia & Giraitis, Liudas, 2016. "Spectral approach to parameter-free unit root testing," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 4-16.
    12. Yongtao Guan, 2008. "A KPSS Test for Stationarity for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 64(3), pages 800-806, September.

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