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

TL;DR

This paper characterizes the asymptotic distributions of sample covariances in large panel data of random-coefficient AR(1) processes, revealing diverse limit behaviors depending on tail properties and growth rates.

Contribution

It provides a complete description of the limit distributions of sample covariances in large panels with random-coefficient AR(1) processes, including stable and non-stable limits.

Findings

Sample covariances exhibit various stable and non-stable limit behaviors.

Limit distributions depend on the tail index $eta$ and the growth rate of N and n.

The results cover cases where the tail distribution is regularly varying at the unit root.

Abstract

The present paper obtains a complete description of the limit distributions of sample covariances in N x 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.