Exit times for some nonlinear autoregressive processes

TL;DR

This paper studies the expected time for certain nonlinear autoregressive processes to exit a bounded interval, extending previous results from linear cases to more general, especially piecewise linear, functions using large deviation principles.

Contribution

It extends existing exit time results from linear autoregressive models to nonlinear, particularly piecewise linear, functions using large deviation techniques.

Findings

Derived formulas for exit times in nonlinear autoregressive processes.

Extended previous linear case results to more general functions.

Focused on piecewise linear functions for broader applicability.

Abstract

By using the large deviation principle, we investigate the expected exit time from the interval [-1,1] of a process of autoregressive type. The case when the autoregression function f is linear and the innovations have a normal distribution has been treated before. In this paper, we extend the results to more general functions f, with the main focus on piecewise linear functions.