A note on stationarity of the MTAR process on the boundary of the stationarity region

We show that the momentum threshold autoregressive (MTAR) process is stationary (ergodic) on the boundary of the region of stationarity corresponding to partial unit roots. This is in contrast with the fact that the self exciting TAR (SETAR) process, as well as the linear autoregressive moving average (ARMA) process, is nonstationary on the boundary of the region of stationarity.