TARCH {tsDyn}R Documentation

Treshold-ARCH model

Description

Treshold AutoRegressive Conditionally Heteroschedastic model

Usage

  tarch(x, m, d=1, steps=d, series, coef, thDelay=0, control=list(), ...)

Arguments

x time series
m, d, steps embedding dimension, time delay, forecasting steps
series time series name (optional)
coef vector of starting coefficients values. If missing, they are randomly generated from the log-normal distribution
thDelay time delay value for thresholding
control, ... additional parameters to be passed to optim

Details

Treshold-ARCH model:

x[t] = sigma[t] eps[t]

with eps[t] standard white noise, and sigma[t] conditional standard deviation which takes the form:

sigma2[t+steps] = ( b[0,0] + sum_j b[0,j] sigma2[t-(j-1)d] ) * (Z[t] <= 0) + ( b[1,0] + sum_j b[1,j] sigma2[t-(j-1)d] ) * (Z[t] > 0)

and Z[t] threshold variable defined as Z[t] = x[t-thDelay*d]. The model is estimated by Conditional Maximum Likelihood, with positivity of parameters restriction (strict for b[0,0] and b[1,0]), using the L-BFGS-B provided by the optim function.

Standard errors provided in the summary are asymptoticals.

No model specific plots are produced by the plot method.

Value

An object of class tarch.

Author(s)

Antonio, Fabio Di Narzo

References

Threshold Arch Models and asymmetries in volatility, R. Rabemanajara and J. M. Zakoian, Journal of Applied Econometrics, vol. 8 (1993)

Threshold heteroschedastic models, J. M. Zakoian, D. P. INSEE (1991)

See Also

setar, lstar

Examples

#
#Taken from tseries::garch man page
#
n <- 1100
a <- c(0.1, 0.5, 0.2)  # ARCH(2) coefficients
e <- rnorm(n)
x <- double(n)
x[1:2] <- rnorm(2, sd = sqrt(a[1]/(1.0-a[2]-a[3])))
for(i in 3:n)  # Generate ARCH(2) process
{
   x[i] <- e[i]*sqrt(a[1]+a[2]*x[i-1]^2+a[3]*x[i-2]^2)
}
x <- ts(x[101:1100])

x.tarch <- tarch(x, m=2)
summary(x.tarch)

[Package tsDyn version 0.5-5 Index]