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

Abstract

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 $|\rho| < 1$, $|\rho| > 1$, and $\rho = 1 + \frac{c}{n^\alpha}$ for some constant $c \in R$ and $\alpha \in (0, 1]$, 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.