A note on the distribution of the least squares estimator of a random walk with drift: Some analytical evidence

In this paper we define the notion of a local drift in a unit root process. The theory provides a bridge between the apparent diverging asymptotic theories that apply when a drift is either present or absent in an integrated time-series. Our asymptotic results help to explain the Monte Carlo results of Hylleberg and Mizon (Economics Letters, 1989, 29, 225–230) and Schmidt (Advances in Econometrics, 1988, 8, 161–200).