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