CIRJE-F-55. Kunitomo, Naoto, "On Ergodicity of Some TAR(2) Processes", July 1999.

We give a set of conditions for the geometrical ergodicity and the non-explosiveness of the solutions in the second-order threshold autoregressive (TAR) processes. We also discuss some conditions for the geometrical ergodicity of the second-order simultaneous switching autoregressive (SSAR) processes. Unlike the linear autoregressive processes and the first-order TAR processes, the ergodic and non-explosive regions become quite complicated even in some special TAR processes.