This paper is concerned with estimation and inference in a univariate p-th order autoregressive model with a time trend and, possibly, a unit root. Econometric interest in uni variate autoregressions is partly due to the direct benefits that are attainable from a better understanding of the time series structures of individual economic variables. In addition, developments in the study of univariate time series typically lead the way to developments in the study of multivariate time series models. There are two fundamental problems that complicate estimation and inference in autoregressive models with a possible unit root (i.e., AR/UR models). First, the ordinary least squares (OLS) estimator is biased and nonnormal in finite samples. Second, the asymptotic distribution of the OLS estimator is discontinuous at the boundary of the parameter space, being normal in the interior but nonstandard at the unit root endpoint.
Roy, Anindya; Falk, Barry; and Fuller, Wayne A., "Estimation of the Trend Model with Autoregressive Errors" (1999). Economic Staff Paper Series. 334.