A Note on Asymptotic Power Calculations in Nearly Nonstationary Time Series

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian motion. Using this result, we point out how standard contiguity arguments can be applied to obtain a representation of the asymptotic power function in nearly nonstationary alternatives.