# 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, , and 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 1 t-1 t | x t-1 |

α 2 2 t-1 t | x t-1 |

Parameters are initially set to

β=-1.5

1

β=-1.5

1

β=0.5

2

x=

t

-1.5x t-1 t | x t-1 |

0.5x t-1 t | x t-1 |

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

E(x)

t