Limit theory for an AR(1) model with intercept and a possible infinite variance

In this paper, we derive the limit distribution of the least squares estimator for an AR(1) model with a non-zero intercept and a possible infinite variance. It turns out that the estimator has a quite different limit for the cases of |ρ | < 1 , |ρ | > 1 , and ρ = 1 + c/n^α for some constant c ∈ R and α∈ (0, 1] , and whether or not the variance of the model errors is infinite also has a great impact on both the convergence rate and the limit distribution of the estimator.