This paper presents optimal tests for parameter instability in the generalized method of moments (GMM) framework. The new tests include tests that are optimal for both one-sided and two-sided alternatives. One of the optimal tests for two-sided alternatives is the GMM generalization of the test presented in Andrews and Ploberger (1994) for the likelihood framework. The new tests include a class of optimal tests that direct the test's power to specific locations in the sample. One of these optimal tests has the attractive feature of a normal distribution under the null hypothesis. Copyright 1996 by The Econometric Society.

Asymptotic distributions are derived for the ordinary least squares estimate of a first order autoregression model when the series is fractionally integrated. The fractional unit root distribution is introduced to describe the limiting distribution. The unit root distribution is shown to be an atypical member of this family because its density is nonzero over the entire real line. For -1/2 Copyright 1990 by The Econometric Society.