On the stationarity of the Threshold Autoregressive process: the two regimes case

This paper deals with the stationarity of the nonlinear Threshold Autoregressive process (TAR) whose self exciting representation (shortly called SETAR) has been widely presented in the literature. Starting from these results, the main aim is the discussion of some theoretical differences between TAR and SETAR models, mainly related to their stationarity. We shortly provide new issues on the stationarity of the TAR model whereas those results are discussed and compared through empirical examples with what well known in the SETAR context.