genETARCH {boodd} | R Documentation |
Generate an Exponential TAR-ARCH Process
Description
Simulates an Exponential Threshold Autoregressive (ETAR)-ARCH process.
Usage
genETARCH(n, alpha1, alpha2, beta)
Arguments
n |
An integer value; the length of the process to simulate. |
alpha1 |
A numeric value; parameter of the process such that |
alpha2 |
A numeric value; parameter of the process driving the behaviour of the process
for small values of |
beta |
A positive numeric value; parameter of the process driving the ARCH effect. |
Details
The ETAR-ARCH process is defined by the equation
X_{t+1} = \left(\alpha_1 + \alpha_2 \exp(-X_t^2)\right)X_t + \sqrt{1 + \beta X_t^2} Z_t
,
where Z_t
is an i.i.d. error sequence.
Value
A numeric vector of length n+1
, containing the simulated values
of the ETAR-ARCH process.
References
Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.
See Also
Examples
etarch = genETARCH(100,0.3,0.8,0.5)
plot(etarch, type="l")