A new approach for analyzing panel AR(1) series with application to the unit root test

Abstract: This paper derives several novel tests to improve on the t-test for testing AR(1) coefficients of panel time series, i.e., of multiple time series, when each has a small number of observations. These tests can determine the acceptance or the rejection of each hypothesis individually while controlling the average type one error. Strikingly, the testing statistics derived by the empirical Bayes approach can be approximated by a simple form similar to the t-statistic; the only difference is that the means and the variances are estimated by shrinkage estimators. Simulations demonstrate that the proposed tests have higher average power than the t-test in all settings we examine including those when the priors are miss-specified and the cross section series are dependent.