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Unit Root Tests Based On Adaptive Maximum Likelihood Estimation

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  • Shin, Dong Wan
  • So, Beong Soo

Abstract

Adaptive maximum likelihood estimators of unit roots in autoregressive processes with possibly non-Gaussian innovations are considered. Unit root tests based on the adaptive estimators are constructed. Limiting distributions of the test statistics are derived, which are linear combinations of two functionals of Brownian motions. A Monte Carlo simulation reveals that the proposed tests have improved powers over the classical Dickey–Fuller tests when the distribution of the innovation is not close to normal. We also compare the proposed tests with those of Lucas (1995, Econometric Theory 11, 331–346) based on M-estimators.

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  • Shin, Dong Wan & So, Beong Soo, 1999. "Unit Root Tests Based On Adaptive Maximum Likelihood Estimation," Econometric Theory, Cambridge University Press, vol. 15(1), pages 1-23, February.
    • Handle: RePEc:cup:etheor:v:15:y:1999:i:01:p:1-23_15
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    Citations

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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. Shiqing Ling & W. K. Li & Michael McAleer, 2003. "Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence," Econometric Reviews, Taylor & Francis Journals, vol. 22(2), pages 179-202.
    3. Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University.
    4. Galvao Jr., Antonio F., 2009. "Unit root quantile autoregression testing using covariates," Journal of Econometrics, Elsevier, vol. 152(2), pages 165-178, October.
    5. Dong Wan Shin & Oesook Lee, 2004. "M‐Estimation for regressions with integrated regressors and arma errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 283-299, March.
    6. Shin, Dong Wan & Park, Soo Jung & Oh, Man-Suk, 2009. "A robust sign test for panel unit roots under cross sectional dependence," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1312-1327, February.
    7. Ted Juhl & Zhijie Xiao, 2000. "N-Consistent Semiparametric Regression: Partially Linear Models with Unit Roots," Econometric Society World Congress 2000 Contributed Papers 1532, Econometric Society.
    8. 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.
    9. Kai Carstensen, 2003. "The finite-sample performance of robust unit root tests," Statistical Papers, Springer, vol. 44(4), pages 469-482, October.
    10. Shin, Dong Wan & So, Beong Soo, 1999. "New tests for unit roots in autoregressive processes with possibly infinite variance errors," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 387-397, October.

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