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Unit Root Tests Based on M Estimators

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  • Lucas, André

Abstract

This paper considers unit root tests based on M estimators. The asymptotic theory for these tests is developed. It is shown how the asymptotic distributions of the tests depend on nuisance parameters and how tests can be constructed that are invariant to these parameters. It is also shown that a particular linear combination of a unit root test based on the ordinary least-squares (OLS) estimator and on an M estimator converges to a normal random variate. The interpretation of this result is discussed. A simulation experiment is described, illustrating the level and power of different unit root tests for several sample sizes and data generating processes. The tests based on M estimators turn out to be more powerful than the OLS-based tests if the innovations are fat-tailed.

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  • Lucas, André, 1995. "Unit Root Tests Based on M Estimators," Econometric Theory, Cambridge University Press, vol. 11(02), pages 331-346, February.
  • Handle: RePEc:cup:etheor:v:11:y:1995:i:02:p:331-346_00
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    5. Phillips, Peter C. B., 1995. "Bayesian model selection and prediction with empirical applications," Journal of Econometrics, Elsevier, vol. 69(1), pages 289-331, September.
    6. Peter C.B. Phillips & Werner Ploberger, 1991. "Time Series Modelling with a Bayesian Frame of Reference: 1. Concepts and Illustrations," Cowles Foundation Discussion Papers 980, Cowles Foundation for Research in Economics, Yale University.
    7. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
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