A test for fractionally integrated time series

Abstract

Recent work by Sowell (1990) and Diebold and Rudebusch (1991a) show that Dickey-Fuller unit root tests can have low power under fractionally integrated alternatives. This paper proposes a locally best test designed particularly to detect such alternatives. The test is based on the asymptotic likelihood function in frequency domain. A Monte Carlo experiment shows that the test is quite powerful, even in small samples.