I have a general understanding of the GARCH model, but I'm confused with two things about the conditional volatility.
The past values of the conditional volatility are given by the updating formula. I ran a model with
garchFit in "fGarch" package in R and extracted the parameters:
alpha = coef(model)["alpha1"] beta = coef(model)["beta1"] w = coef(model)["omega"]
I then calculated by hand the value of the conditional variance at time
t=3 (just an example):
w + email@example.com + beta*squaredReturns
It gave me
0.0002843326. However, this is different
from firstname.lastname@example.org, which equals
0.000284847. Of course it is a small difference, but since I thought that this equation was exactly the way the
email@example.com (conditional variance) was calculated, then I'm definitely missing something.
My second question has to do with the initialization. If this equation is indeed the way the conditional variance is calculated, then how is the value in
t=1 calculated, since there are no values for return and variance in