Second-order continuous-time non-stationary Gaussian autoregression

TL;DR

This paper explores the asymptotic behavior of maximum likelihood estimators in second-order Gaussian autoregressive differential equations, focusing on non-ergodic cases where roots are not in the left half-plane.

Contribution

It provides a comprehensive analysis of all possible asymptotic behaviors of estimators in non-stationary second-order Gaussian ODE models.

Findings

Classifies asymptotic behaviors in non-ergodic cases

Identifies conditions for different estimator limits

Extends understanding of non-stationary Gaussian processes

Abstract

The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven by Gaussian white noise. The emphasis is on the non-ergodic case, when the roots of the corresponding characteristic equation are not both in the left half-plane.