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 |alpha1|<1.

alpha2

A numeric value; parameter of the process driving the behaviour of the process for small values of x. |alpha1+alpha2| may be bigger than 1.

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

genMM1, zi_inar_process.

Examples

etarch = genETARCH(100,0.3,0.8,0.5) 
plot(etarch, type="l")


[Package boodd version 0.1 Index]