An autoregressive model leading to stable distributions

TL;DR

This paper introduces an autoregressive model with random coefficients that, when normalized, converges to a stable distribution, providing insights into the behavior of such stochastic processes.

Contribution

The paper presents a novel autoregressive model with random coefficients that yields a stable distribution as its stationary limit, expanding understanding of stable processes.

Findings

Model converges to a stable distribution after normalization

Stationary distribution identified as stable

Provides a new approach to modeling with stable limits

Abstract

We construct an autoregressive model with random coefficients that has a stationary distribution after proper normalization. This limit distribution is found to be stable.