One popular class of nonlinear time series models is the threshold autoregressive (TAR) model, which looks very similar to the Markov switching models. Using regression methods, simple AR models are arguably the most popular models to explain nonlinear behavior. Regimes in the threshold model are determined by past, d, values of its own time series, relative to a threshold value, c.
The following is an example of a self-exciting TAR (SETAR) model. The SETAR model is self-exciting because switching between different regimes depends on the past values of its own time series:
Using dummy variables, the SETAR ...
