Asymptotic Properties of Self-Normalized Linear Processes with Long Memory

TL;DR

This paper investigates the convergence of long memory linear processes with heavy-tailed innovations to fractional Brownian motion, providing a self-normalized version relevant for economic models with infinite variance innovations.

Contribution

It introduces a self-normalized limit theorem for long memory linear processes with infinite variance innovations, extending existing results to more realistic heavy-tailed scenarios.

Findings

Convergence to fractional Brownian motion established for processes with infinite variance innovations.

Derived a self-normalized version of the limit theorem applicable in practical economic models.

Provides theoretical foundation for analyzing long memory processes with heavy tails.

Abstract

In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem. The study is motivated by models arising in economical applications where often the linear processes have long memory, and the innovations have heavy tails.