Interpreting coefficients of rugarch package in R

Question

How do I interpret the coefficients of t garch in the rugarch package?

which is the parameter for dummy variable? and also which one is the coefficient for arch and garch parameter

I have the results however I am confused the dummy variable parameter

spec = rugarch::ugarchspec(variance.model = list(model = "fGARCH", garchOrder = c(1,1), submodel = "TGARCH"), mean.model = list(armaOrder = c(1,1), include.mean = TRUE),distribution.model = "std")

fgarch.t = rugarch::ugarchfit(data = daily_ret_developed_monthly, 
                              spec = spec, solver = "solnp")

fgarch.t@fit$coef



 mu           ar1           ma1         omega        alpha1         beta1         eta11         shape 
 0.0008409928  0.8470773484 -0.8553335918  0.0001488852  0.0816275946  0.9317382995 -0.1644055512  3.6871423500

Answer 1

The short answer is:

1. eta11 is the rotation parameter, ie when you do decomposition of the residuals inside the equation for the conditional variance, you can allow a shift ( eta2 ) or/and rotation ( eta1 ) in the news impact curve .
2. alpha1 is the ARCH(q) parameter. In your case, q is 1.
3. beta1 is the GARCH(p) parameter. In your case, p is 1.

Additional information :

You are looking at the following family of GARCH equations, collectively called fGARCH in rugarch package:

---

---

For threshold GARCH ( tGARCH ) models:

and

while

You have also mu parameter estimated since you have selected include.mean = TRUE . The parameter shape is a numeric value denoting the shape parameter of the conditional distribution of standardized residuals z_t . Lastly, the parameter omega in your model is the variance intercept parameter .

Hope this helps.