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.

21pages