# Two-Regime Threshold Autoregressive Model Simulation

Two-Regime Threshold Autoregressive Model Simulation

This Demonstration allows you to study realizations from a two-regime threshold autoregressive (TAR) process of the first order by changing its parameters. The two-regime TAR(1) model is represented by:=

Parameters are initially set to =-1.5, =-1.5, and =0.5 to obtain the following two-regime TAR(1) process: =

Note that the process is stationary and geometrically ergodic despite the coefficient -1.5 in the first regime. The series contains large upward jumps when it becomes negative (due to the -1.5 coefficient) and there are more positive than negative jumps. The model also contains no constant term, but is not zero.

x

t

α 1 β 1 x t-1 ϵ t | x t-1 |

α 2 β 2 x t-1 ϵ t | x t-1 |

β

1

β

1

β

2

x

t

-1.5 x t-1 ϵ t | x t-1 |

0.5 x t-1 ϵ t | x t-1 |

E()

x

t