STAR model

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.

Exponential transition function for the ESTAR model with varying from -10 to +10 and - from 0 to 1.
Exponential transition function for the ESTAR model with varying from -10 to +10, from 0 to 1 and two exponential roots ( and ) equal to -7 and +3.
Logistic transition function for the ESTAR model with varying from -10 to +10 and - from 0 to 1. Calculated using GNU R package.