A comparative study on p value combination tests for unit roots in multiple time series

This note offers a Monte Carlo investigation of the performance of nine p value combination methods for unit root testing in multiple time series using a novel approach to simulation. Rather than on time series, simulations are based on random draws of Dickey-Fuller p values under the null and under local alternatives. This makes it possible to investigate the properties of the different combiners under ideal conditions in which small sample effects and possible model misspecification issues have no role. The results show that no combination approach delivers a uniformly best test in the presence of independent p values. However, the probit combination method and the sum method on average outperform the other combiners within the unit root setting. The performance of the combination tests is generally unsatisfactory in the presence of cross-correlated p values.