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# 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.

### DETAILS

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

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