TARCH {tsDyn} | R Documentation |
Treshold AutoRegressive Conditionally Heteroschedastic model
tarch(x, m, d=1, steps=d, series, coef, thDelay=0, control=list(), ...)
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 |
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.
An object of class tarch
.
Antonio, Fabio Di Narzo
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)
# #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)