Exit times for multivariate autoregressive processes

TL;DR

This paper analyzes the asymptotic behavior of exit times for multivariate autoregressive processes with Gaussian noise, revealing dependence on the set and covariance, and extends results to univariate cases.

Contribution

It provides a novel analysis of exit times using large deviation principles for multivariate autoregressive processes, including univariate extensions.

Findings

Exit times depend only on the set and covariance matrix.

Asymptotic behavior is characterized by large deviation principles.

Results apply to both multivariate and univariate autoregressive processes.

Abstract

We study exit times from a set for a family of multivariate autoregressive processes with normally distributed noise. By using the large deviation principle, and other methods, we show that the asymptotic behavior of the exit time depends only on the set itself and on the covariance matrix of the stationary distribution of the process. The results are extended to exit times from intervals for the univariate autoregressive process of order n, where the exit time is of the same order of magnitude as the exponential of the inverse of the variance of the stationary distribution.