A discussion on power of ADF F-test with unexpected initial value

Abstract

This article attempts to show when the series is a stationary autoregressive process, of which, the initial value is far from the deterministic trend, power of Augmented Dickey-Fuller(ADF) F-test is not only superior to the tests, which are most powerful for small and moderate initial value, such as GLS-DF test (Elliott et al., 1996) but also to ADF t-test, given small and moderate sample sizes; and especially, when the autoregressive coefficient is close to unity. The procedure proposed by Holden and Perman (1994), which takes advantage of both t- and F-type ADF tests is recommended.