  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.
