Testing for a Trend with Persistent Errors

We develop new tests for the coe¢ cient on a time trend in a regression of a variable on a constant and time trend where there is potentially strong serial correlation. This serial correlation can also include a unit root. We obtain tests under two different assumptions on the initial value for the stochastic component of the variable being examined, either this being zero asymptotically (as in previous examinations of this hypothesis) and also allowing the initial condition to be drawn from its unconditional distribution. We …nd that statistics perform better under the second of these assumptions, which is the more natural assumption to make. JEL classi…cation: C12; C21; C22