Convergence of averages of scaled functions of I(1) linear processes

Econometricians typically make use of functional central limit theorems to prove results for I(1) processes. For example, to establish the limit distr ibutions of unit root tests such as the Phillips-Perron and Dickey-Fuller t ests, the functional central limit theorem plays a crucial role. In this pa per, it is pointed out that for linear processes, minimal conditions that e nsure that only a central limit theorem holds are sufficient for establishi ng limit distributions of such tests. This eliminates the need to impose th e stronger functional central limit theorem conditions and implies converge nce of Dickey-Fuller type unit root tests under minimal conditions. (C) 200 1 Elsevier Science B.V. All rights reserved.