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

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.