Finite-sample distribution of the augmented Dickey–Fuller test with lag optimization

Abstract

This article presents a response surface analysis for the distribution of the augmented Dickey–Fuller (ADF) test with optimized lag order in the autoregression using frequently applied data-dependent methods. Simulation results demonstrate that finite-sample distribution of the test depends critically on the lag-order determination rule. The univariate test and its panel counterparts exhibit size distortion when the lag order in the autoregression is optimized but inappropriate distribution is employed in test implementation. Response surface coefficients reported for the finite-sample distribution of the test with lag optimization are therefore useful tools for practitioners in applied research. The simulation evidence and practical use of the response surface coefficients are substantiated with empirical illustrations.

Keywords:

• unit root test
• lag optimization
• response surface
• Monte Carlo

JEL Classification::

• C12
• C15
• C22
• C23

Acknowledgements

Earlier versions of this article under different titles were presented at the 2nd International Workshop on Computational and Financial Econometrics, Neuchatel, 2008, and the 15th International Conference on Computing in Economics and Finance, Sydney, 2009. The author thanks participants in the conferences for their helpful comments. The author also gratefully acknowledges financial support from the Research Committee of the University of Macau under research grant no. RG001/08-09S/11T/TPS/FBA, and conference grant nos. CG100/07-08S/TPS/FBA and CG036/08-09S/TPS/FBA.