Tail behaviours of multiple-regime threshold AR models with heavy-tailed innovations

Abstract This paper studies the tail behaviours of the stationary distribution of multiple-regime threshold AR models with multiple heavy-tailed innovations. It is shown that the marginal tail probability has the same order as that of the innovation with the heaviest tail. Other new results in this paper include the geometric ergodicity and the tail dependence of TAR models with multiple heavy-tailed innovations.