Probabilistic properties of Self Exciting Threshold Autoregressive processes
In the present paper we focus the attention on the ergodicity (and stationarity) of the Self Exciting Autoregressive (SETAR) process. In more detail we review and compare the results given in the literature highlighting the main theoretical issues. Starting from these contributions, we debate, taking advantage of case studies, on the opportunity to further investigate on the statistical properties of the SETAR models and in particular on the possibility to weaken its stationarity conditions.