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Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power

Published online by Cambridge University Press:  11 February 2009

Bruce E. Hansen
Bruce E. Hansen
Affiliation:
Boston College
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Abstract

In the context of testing for a unit root in a univariate time series, the convention is to ignore information in related time series. This paper shows that this convention is quite costly, as large power gains can be achieved by including correlated stationary covariates in the regression equation.

The paper derives the asymptotic distribution of ordinary least-squares estimates of the largest autoregressive root and its t-statistic. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but a convex combination of the Dickey-Fuller distribution and the standard normal, the mixture depending on the correlation between the equation error and the regression covariates. The local asymptotic power functions associated with these test statistics suggest enormous gains over the conventional unit root tests. A simulation study and empirical application illustrate the potential of the new approach.

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 5 , October 1995 , pp. 1148 - 1171
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.Google Scholar
Berk, K.N. (1974) Consistent autoregressive spectral estimates. Annals of Statistics 2, 489–502.CrossRefGoogle Scholar
Chan, N.H. & Wei, C.Z. (1987) Asymptotic inference for nearly nonstationary AR(1) processes. The Annals of Statistics 15, 1050–1063.Google Scholar
Elliott, G., Rothenberg, T.J., & Stock, J.H. (1992) Efficient Tests for an Autoregressive Unit Root. Manuscript. Harvard University.Google Scholar
Engle, R.F. & Granger, C.W.J. (1987) Co-integration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.Google Scholar
Hansen, B.E. (1992a) Consistent covariance matrix estimation for dependent heterogeneous processes. Econometrica 60, 967–972.CrossRefGoogle Scholar
Hansen, B.E. (1992b) Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8, 489–500.CrossRefGoogle Scholar
Herrndorf, N. (1984) A functional central limit theorem for weakly dependent sequences of random variables. Annals of Probability 12, 141–153.CrossRefGoogle Scholar
Horvath, M.T. & Watson, M.W. (1993) Testing for Cointegration When Some of the Cointegrating Vectors Are Known. Working paper 93–25, Federal Reserve Bank of Chicago.Google Scholar
Johansen, S. & Juselius, K. (1992) Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for the UK. Journal of Econometrics 53, 211–244.Google Scholar
Kremers, J.J.M., Ericsson, N.R., & Dolado, J.J. (1992) The power of cointegration tests. Oxford Bulletin of Economics and Statistics 54, 325–348.CrossRefGoogle Scholar
Nelson, C.R. & Plosser, C.I. (1982) Trends and random walks in macroeconomic time series. Journal of Monetary Economics 10, 139–162.CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1994) Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61, 631–653.Google Scholar
Phillips, P.C.B. (1987) Toward a unified asymptotic theory for autoregression. Biometrika 74, 535–547.CrossRefGoogle Scholar
Phillips, P.C.B. & Ouliaris, S. (1990) Asymptotic properties of residual based tests for cointegration. Econometrica 58, 165–193.Google Scholar
Said, S.E. & Dickey, D.A. (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71, 599–608.CrossRefGoogle Scholar
Schotman, P.C. & van Dijk, H.K. (1991) On Bayesian routes to unit roots. Journal of Applied Econometrics 6, 387–401.CrossRefGoogle Scholar