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


Author Info

  • Bruce E. Hansen

    (Boston College)


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 (OLS) 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.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 300..

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Date of creation: May 1995
Date of revision:
Publication status: Published in Econometric Theory, 1995, 11:1148-1172
Handle: RePEc:boc:bocoec:300

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Keywords: Time series modeling; unit roots;

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