Near-integration and deterministic trends

In this paper we seek to analyze the implications for estimation and inference within the Dickey-Fuller class of models when time series contain a root local to unity. We extend the results previously obtained in the literature to models with maintained deterministic components and especially the ability of conducting inference on the deterministic elements is focused. The approach undertaken also helps bridging the discontinuity in limiting distributions that usually apply when roots lie exactly on the unit circle, as opposed to roots strictly less than unity. The paper is completed by simulating some of the distributions suggested by the asymptotic theory to see how well these approximate the actual finite sample distributions.