Sample autocovariances of long-memory time series

TL;DR

This paper investigates the asymptotic behavior of sample autocovariances in long-memory time series, revealing different convergence rates and limit distributions depending on moment conditions and dependence strength.

Contribution

It characterizes the asymptotic distributions of sample autocovariances under various moment and dependence assumptions, highlighting cases where normal approximation fails.

Findings

Identifies three types of convergence rates and limit distributions.

Shows normal approximation does not always hold in practical scenarios.

Provides theoretical insights into long-memory process autocovariance behavior.

Abstract

We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three types of convergence rates and limit distributions. In particular, a normal approximation with the standard rate does not always hold in practically relevant cases.