Correction to: A Smooth Transition Autoregressive Model for Matrix-Variate Time Series

Abstract

This note aims to correct a too strong generalization in the proof of Proposition 1. In the initially published version of this article, the proof of Proposition 1 incorrectly stated that the spectral radius of a sum of two general square matrices, W 1 and W 2 , is bounded by the maximum of the spectral radii of each matrix. Nevertheless, this statement does not hold in general for any type of square matrix, which means that there can be cases in which the inequality in the published proof does not hold. For a general stationarity condition, we can rely on the findings of Kheifets and Saikkonen (2020), which lead to the following proposition.