Stationarity and ergodicity of vector STAR models

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.

Accepted to Econometric Reviews

References in corpus (1)

• Multivariate Specification Tests Based on a Dynamic Rosenblatt Transform

Cited by in corpus (1)

• Identification by non-Gaussianity in structural threshold and smooth transition vector autoregressive models