GARCH (Pro.)

mean
is the GARCH model mean (i.e. mu).

alphas
are the parameters of the ARCH(p) component model (starting with the lowest lag).

betas
are the parameters of the GARCH(q) component model (starting with the lowest lag).

innovation
is the probability distribution function of the innovations/residuals (1=Gaussian, 2=t-Distribution, 3=GEDⁱ). If missing, a gaussian distribution is assumed.

v
is the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function.

1. The underlying model is described here.
2. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
3. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
4. The GARCH function returns an array of size p+q+7 in the following order:
   1. 
   2. 
   3. 
   4. Innovation type (1=Normal, 2=Student's t, 3=GED)
   5. 
   6. shape parameter (degrees of freedom).
   7. 
   8. 

• Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740

• Wikipedia - Autoregressive conditional heteroskedasticity