Two-Regime Threshold Autoregressive Model Simulation

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.

Contributed by: Jozef Barunik (March 2011)
Open content licensed under CC BY-NC-SA



The TAR model is motivated by empirically observed nonlinear characteristics such as asymmetry in declining and rising patterns of a process. It is used for financial time series modeling. The model uses a simple threshold to improve linear approximation.

More information about TAR processes can by found at:

R. S. Tsay, Analysis of Financial Time Series, New York: Wiley, 2001.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.