Multivariate Self-Exciting Threshold Autoregressive Models with eXogenous Input

This study defines a multivariate Self--Exciting Threshold Autoregressive with eXogenous input (MSETARX) models and present an estimation procedure for the parameters. The conditions for stationarity of the nonlinear MSETARX models is provided. In particular, the efficiency of an adaptive parameter estimation algorithm and LSE (least squares estimate) algorithm for this class of models is then provided via simulations.