On stationarity and ββ-mixing of periodic bilinear processes

This paper studies some probabilistic properties of periodic bilinear processes. In these nonlinear models, the parameters are allowed to switch between different regimes. Stationarity and geometric ergodicity conditions (in periodic sense) are given under general and tractable assumptions. We use these results to give necessary and sufficient conditions for stationarity of specific periodic GARCH processes which can be written as a periodic bilinear models. Moreover, it is shown that local stationarity i.e., stationarity within each regime, is not necessary to obtain global stationarity.