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Limit theory for an AR(1) model with intercept and a possible infinite variance
Qing Liu, Xiaohui Liu · 2018-02-28 · via math.ST updates on arXiv.org

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 $ρ= 1 + \frac{c}{n^α}$ for some constant $c \in R$ and $α\in (0, 1]$, 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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