The transition might depend on the past values of the x series (similar to the SETAR models), or exogenous variables.
The model consists of 2 autoregressive (AR) parts linked by the transition function.
Consider a simple AR(p) model for a time series yt where: written in a following vector form: where: STAR models were introduced and comprehensively developed by Kung-sik Chan and Howell Tong in 1986 (esp.
Such a test is important before adopting a STAR model because, among other issues, the parameter controlling its rate of switching is notoriously data-hungry.
In both cases the presence of the transition function is the defining feature of the model as it allows for changes in values of the parameters.