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Two-Regime Threshold Autoregressive Model Simulation

​
threshold parameter
threshold k
0
parameters of first AR(1) process
α
1
0
β
1
-1.5
parameters of second AR(1) process
α
2
0
β
2
0.5
new random case
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:​​
x
t
=
α
1
+
β
1
x
t-1
+
ϵ
t
x
t-1
<k
α
2
+
β
2
x
t-1
+
ϵ
t
x
t-1
≥k
​Parameters are initially set to
β
1
=-1.5
,
β
1
=-1.5
, and
β
2
=0.5
to obtain the following two-regime TAR(1) process:
x
t
=
-1.5
x
t-1
+
ϵ
t
x
t-1
<0
0.5
x
t-1
+
ϵ
t
x
t-1
≥0
​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
)
is not zero.
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