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Tests for Asymmetry in Possibly Nonstationary Time Series Data


  • Shin, Dong Wan
  • Lee, Oesook


Tests for asymmetric adjustment in possibly nonstationary, nearly nonstationary, or stationary time series data are developed. The asymmetry is modeled by the momentum threshold autoregressive model of Enders and Granger and an extension of it. The tests are t-type tests and Wald tests based on instrumental-variable estimators and are asymptotically normal or chi-squared regardless of stationarity/nonstationarity of data-generating processes. This is in contrast to the fact that the t tests and the Wald tests based on the ordinary least squares estimator (OLSE) are asymptotically normal and chi-squared, respectively, only under stationarity and are thus statistically invalid under nonstationarity. A Monte Carlo simulation shows that the proposed tests have stable sizes. Powers of the proposed tests against stationary alternatives are comparable to those of the OLSE-based tests. The Monte Carlo study also shows that the new estimators are less biased than the OLSE when data-generating processes are random walks. The proposed tests are applied to a monthly U.K. interest-rate dataset to find evidences for asymmetry in directions of adjustments as well as in amounts of adjustments.

Suggested Citation

  • 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 233-244, April.
  • Handle: RePEc:bes:jnlbes:v:19:y:2001:i:2:p:233-44

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    References listed on IDEAS

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    Cited by:

    1. So, Beong Soo & Shin, Dong Wan, 2001. "An invariant sign test for random walks based on recursive median adjustment," Journal of Econometrics, Elsevier, vol. 102(2), pages 197-229, June.
    2. Frédérique Bec & Mélika Ben Salem & Ronald MacDonald, 2006. "Real exchange rates and real interest rates : a nonlinear perspective," Recherches économiques de Louvain, De Boeck Université, vol. 72(2), pages 177-194.
    3. 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.
    4. Shin, Dong Wan & Lee, Oesook, 2007. "Asymmetry and nonstationarity for a seasonal time series model," Journal of Econometrics, Elsevier, vol. 136(1), pages 89-114, January.
    5. Dimitris Christopoulos, 2004. "Does Stationarity Characterize Real GDP Movements? Results from Non-Linear Unit Root Tests," Macroeconomics 0406002, EconWPA.
    6. Shin, Dong Wan & So, Beong Soo, 2002. "Recursive mean adjustment and tests for nonstationarities," Economics Letters, Elsevier, vol. 75(2), pages 203-208, April.
    7. Robert, Anderton & Baldwin, Richard & Taglioni, Daria, 2007. "The impact of monetary union on trade prices," Journal of Financial Transformation, Capco Institute, vol. 19, pages 35-48.
    8. Dong Shin & Oesook Lee, 2008. "Unit root tests for panel MTAR model with cross-sectionally dependent error," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 315-326, April.
    9. Shin, Dong Wan & Park, Sangun, 2010. "Robust panel unit root tests for cross-sectionally dependent multiple time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2801-2813, November.
    10. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    11. 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.
    12. Shin, Dong Wan & Kang, Seungho, 2006. "An instrumental variable approach for panel unit root tests under cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 134(1), pages 215-234, September.
    13. Wan Shin, Dong & Lee, Oesook, 2003. "An instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models," Journal of Econometrics, Elsevier, vol. 115(1), pages 29-52, July.
    14. Park, Soo Jung & Wan Shin, Dong & Uk Park, Byeong & Chul Kim, Woo & Oh, Man-Suk, 2005. "Bayesian test for asymmetry and nonstationarity in MTAR model with possibly incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1192-1204, June.
    15. James K. Self, 2006. "Asymmetric Stationarity in National Stock Market Indices: An MTAR Analysis," The Journal of Business, University of Chicago Press, vol. 79(6), pages 3153-3174, November.
    16. Dimitris Christopoulos, 2006. "Does a non-linear mean reverting process characterize real GDP movements?," Empirical Economics, Springer, vol. 31(3), pages 601-611, September.
    17. Christopoulos, Dimitris & León-Ledesma, Miguel A., 2010. "Current account sustainability in the US: What did we really know about it?," Journal of International Money and Finance, Elsevier, vol. 29(3), pages 442-459, April.
    18. Man-Suk Oh & Dong Wan Shin, 2002. "Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 771-789.
    19. Lee, Yonghee & Shin, Dong Wan, 2006. "Unit root tests for cross-sectionally dependent seasonal panels," Economics Letters, Elsevier, vol. 93(3), pages 311-317, December.
    20. Park, Soo Jung & Shin, Dong Wan, 2006. "A sign test for unit roots in a momentum threshold autoregressive process," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 986-990, May.
    21. Wan Shin, Dong & Jhee, Won-Chul, 2006. "Tests for asymmetry in possibly nonstationary dynamic panel models," Economics Letters, Elsevier, vol. 91(1), pages 15-20, April.

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