On the geometric ergodicity of nonlinear multivariate time series

TL;DR

This paper establishes simple conditions ensuring the geometric ergodicity of multivariate nonlinear time series, including models with degenerate coefficients and discontinuities, with applications to BEKK-ARCH(1) models.

Contribution

It provides new, easy-to-verify criteria for irreducibility, T-chain regularity, and geometric ergodicity in complex nonlinear multivariate processes.

Findings

Conditions for irreducibility and regularity are derived.

Results apply to nonlinear BEKK-ARCH(1) models.

Enhances understanding of stability in nonlinear multivariate time series.

Abstract

In this paper we consider multivariate time series obtained as solution to multidimensional nonlinear stochastic difference equations whose coefficients are allowed to be locally degenerate and to present discontinuities. We provide simple and easy to check sufficient conditions for the irreducibility, T-chain regularity and geometric ergodicity of these processes and apply the results to the BEKK-ARCH(1) models with a nonlinear autoregressive term.