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.

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.