Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power
- 1 October 1995
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 11 (5) , 1148-1171
- https://doi.org/10.1017/s0266466600009993
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.Keywords
All Related Versions
This publication has 18 references indexed in Scilit:
- Efficient Tests for an Autoregressive Unit RootEconometrica, 1996
- Convergence to Stochastic Integrals for Dependent Heterogeneous ProcessesEconometric Theory, 1992
- THE POWER OF COINTEGRATION TESTSOxford Bulletin of Economics and Statistics, 1992
- Consistent Covariance Matrix Estimation for Dependent Heterogeneous ProcessesEconometrica, 1992
- On Bayesian routes to unit rootsJournal of Applied Econometrics, 1991
- Asymptotic Properties of Residual Based Tests for CointegrationEconometrica, 1990
- Co-Integration and Error Correction: Representation, Estimation, and TestingEconometrica, 1987
- Testing for unit roots in autoregressive-moving average models of unknown orderBiometrika, 1984
- A Functional Central Limit Theorem for Weakly Dependent Sequences of Random VariablesThe Annals of Probability, 1984
- Consistent Autoregressive Spectral EstimatesThe Annals of Statistics, 1974