Abstract
Although some unified inferences for the coefficient in an AR(1) model have been proposed in the literature, it remains open as to how to construct a unified confidence region for the intercept and the coefficient jointly without a prior on whether the sequence is stationary or unit root or near unit root or moderate deviations from a unit root or explosive and whether the sequence has a zero or nonzero constant intercept. After deriving the joint limit of the least squares estimator for all of these cases, this article proposes a unified empirical likelihood confidence region by first splitting the data into two parts and then constructing some weighted score equations. The good finite sample performance of the proposed method is demonstrated via a simulation study. Real data applications are provided as well.
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