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Unit Root Tests Based on MEstimators

Published online by Cambridge University Press:  11 February 2009

André Lucas
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Abstract

This paper considers unit root tests based on Mestimators. The asymptotic theory for these tests isdeveloped. It is shown how the asymptoticdistributions of the tests depend on nuisanceparameters and how tests can be constructed that areinvariant to these parameters. It is also shown thata particular linear combination of a unit root testbased on the ordinary least-squares (OLS) estimatorand on an M estimator converges to a normal randomvariate. The interpretation of this result isdiscussed. A simulation experiment is described,illustrating the level and power of different unitroot tests for several sample sizes and datagenerating processes. The tests based on Mestimators turn out to be more powerful than theOLS-based tests if the innovations arefat-tailed.

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Type
Research Article
Information
Econometric Theory , Volume 11 , Issue 2 , February 1995 , pp. 331 - 346
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

Andrews, D.W.K. & Monahan, J.C. (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60, 953–966.10.2307/2951574CrossRefGoogle Scholar
Campbell, J.Y. & Perron, P. (1991) Pitfalls and opportunities: What macroeconomists should know about unit roots. In Blanchard, O.J. & Fischer, S. (eds.), NBER Macroeconomics Annual, pp. 141–200. Cambridge, MA: MIT Press.Google Scholar
Cox, D.D. & Llatas, I. (1991) Maximum likelihood type estimation for nearly nonstationary autoregressive time series. Annals of Statistics 19, 1109–1128.10.1214/aos/1176348240CrossRefGoogle Scholar
Davis, R.A., Knight, K. & Liu, J. (1992) M-estimation for autoregressions with infinite variance. Stochastic Processes and Their Applications 40, 145–180.10.1016/0304-4149(92)90142-DGoogle Scholar
Dickey, D.A. & Fuller, W.A. (1979) Distribution of estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431.Google Scholar
Diebold, F.X. & Nerlove, M. (1990) Unit roots in economic time series: A selective survey. Advances in Econometrics 8, 3–69.Google Scholar
Doob, J.L. (1960) Stochastic Processes. New York: Wiley.Google Scholar
Franses, P.H. & Haldrup, N. (1993) The Effects of Additive Outliers on Tests for Unit Roots and Cointegration. Working paper 93/16, European University Institute, Florence.Google Scholar
Fuller, W.A. (1976) Introduction to Statistical Time Series. New York: Wiley.Google Scholar
Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. & Stahel, W.A. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.Google Scholar
Hansen, B.E. (1992) Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8, 489–500.10.1017/S0266466600013189CrossRefGoogle Scholar
Herce, M.A. (1993) Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors. Mimeo, University of North Carolina at Chapel Hill.Google Scholar
Hoek, H., Lucas, A. & van Dijk, H.K. (1994) Classical and Bayesian Aspects of Robust Unit Root Inference. Working paper TI 94–3, Tinbergen Institute, Rotterdam.Google Scholar
Huber, P.J. (1981) Robust Statistics. New York: Wiley.10.1002/0471725250CrossRefGoogle Scholar
Ibragimov, I.A. & Linnik, Yu.V. (1971) Independent and Stationary Sequences of Random Variables. Groningen: Wolters-Noordhoff.Google Scholar
Knight, K. (1989) Limit theory for autoregressive parameters in an infinite variance random walk. Canadian Journal of Statistics 17, 261–278.10.2307/3315522CrossRefGoogle Scholar
Knight, K. (1991) Limit theory for M-estimates in an integrated infinite variance process. Econometric Theory 7, 200–212.10.1017/S0266466600004400CrossRefGoogle Scholar
Lucas, A. (1994) An outlier robust unit root test with an application to the extended Nelson-Plosser data. Journal of Econometrics 66, 153–174.10.1016/0304-4076(94)01613-5CrossRefGoogle Scholar
MacKinnon, J.G. (1992) Model specification tests and artificial regressions. Journal of Economic Literature 30, 102–146.Google Scholar
Martin, R.D. & Yohai, V.J. (1986) Influence functionals for time series. Annals of Statistics 14, 781–818.Google Scholar
Newey, W.K. & West, K.D. (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708.10.2307/1913610Google Scholar
Park, J.Y. & Phillips, P.C.B. (1988) Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4, 468–497.10.1017/S0266466600013402Google Scholar
Phillips, P.C.B. (1987) Time series regression with a unit root. Econometrica 55, 277–301.10.2307/1913237CrossRefGoogle Scholar
Phillips, P.C.B. & Durlauf, S.N. (1986) Multiple time series regression with integrated processes. Review of Economic Studies 53, 473–495.10.2307/2297602CrossRefGoogle Scholar
Phillips, P.C.B. & Perron, P. (1988) Testing for a unit root in time series regression. Biometrika 75, 335–346.10.1093/biomet/75.2.335CrossRefGoogle Scholar
Simpson, D.G., Ruppert, D. & Carroll, R.J. (1992) On one-step GM estimates and stability of inferences in linear regression. Journal of the American Statistical Association 87, 439–450.10.1080/01621459.1992.10475224CrossRefGoogle Scholar
Stock, J.H. (1992) Unit Roots and Trend Breaks. Mimeo, Harvard University, Massachusetts.Google Scholar
White, H. (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 817–838.10.2307/1912934Google Scholar
White, H. (1984) Asymptotic Theory for Econometricians. Orlando, Florida: Academic Press.Google Scholar
Yohai, V.J. (1987) High breakdown-point and high efficiency robust estimates for regression. Annals of Statistics 15, 642–656.10.1214/aos/1176350366Google Scholar