Stationarity and ergodicity of vector STAR models

TL;DR

This paper establishes conditions for the stationarity and ergodicity of vector STAR models, enabling more reliable modeling of nonlinear multivariate time series by verifying key spectral properties.

Contribution

It introduces a novel criterion based on the joint spectral radius for assessing stationarity and ergodicity in vector STAR models.

Findings

Joint spectral radius condition ensures stationarity

Computational tools can verify model properties

Enhances reliability of nonlinear time series analysis

Abstract

Smooth transition autoregressive models are widely used to capture nonlinearities in univariate and multivariate time series. Existence of stationary solution is typically assumed, implicitly or explicitly. In this paper we describe conditions for stationarity and ergodicity of vector STAR models. The key condition is that the joint spectral radius of certain matrices is below 1, which is not guaranteed if only separate spectral radii are below 1. Our result allows to use recently introduced toolboxes from computational mathematics to verify the stationarity and ergodicity of vector STAR models.