An alternative sequential method for the state estimation of a partially observed SETAR(1) process

Abstract

We discuss a novel sequential test based on the quadratic variation of the observations to decide which regime governs the dynamics of the non-observed process in a filtering problem with small observation noise. The non-observed state process is a self-exciting threshold autoregressive process of order one (SETAR(1)) with two regimes. The observation function is not one-to-one. The proposed procedure performs well and may be competitive in some applications.