Testing for a unit root in the presence of moving average errors

In this paper we propose a new approach to testing for unit roots in a time series {yt} with moving average innovations based on an instrumental variable estimator. If {yt} is a random walk with moving average innovations, we derive the limiting distribution of the instrumental variable estimator when the estimated model is either (i) the true model, (ii) a random walk with shift in mean, or (iii) a random walk with shift in mean and a linear time trend. These distributions are identical to those tabulated by Dickey & Fuller (1979, 1981) in some cases, and easily transformed, in the spirit of Phillips (1987), to the Dickey & Fuller distributions in others.