Perfect simulation of autoregressive models with infinite memory

TL;DR

This paper investigates conditions for the uniqueness of the law of binary processes with infinite memory, providing criteria and a perfect simulation algorithm for cases where the transition kernels depend linearly on the entire past.

Contribution

It introduces new sufficient conditions for uniqueness and non-uniqueness of the process law, along with a perfect simulation method for the unique case.

Findings

Provided criteria for uniqueness and non-uniqueness

Developed a perfect simulation algorithm for the unique case

Extended understanding of processes with transition kernels near 0 and 1

Abstract

In this paper we consider the problem of determining the law of binary stochastic processes from transition kernels depending on the whole past. These kernels are linear in the past values of the process. They are allowed to assume values close to both 0 and 1, preventing the application of usual results on uniqueness. More precisely we give sufficient conditions for uniqueness and non-uniqueness. In the former case a perfect simulation algorithm is also given.