Sample covariances of random-coefficient AR(1) panel model

The present paper obtains a complete description of the limit distributions of sample covariances in $N \times n$ panel data when $N$ and $n$ jointly increase, possibly at different rate. The panel is formed by $N$ independent samples of length $n$ from random-coefficient AR(1) process with the tail distribution function of the random coefficient regularly varying at the unit root with exponent $\beta >0$. We show that for $\beta \in (0, 2)$ the sample covariances may display a variety of stable and non-stable limit behaviors with stability parameter depending on $\beta$ and the mutual increase rate of $N$ and $n$.