Chapter 2: FAQs 167
difficulties in practice. These difficulties can be associ-
ated with
- having insufficient data;
- the (log)likelihood function being very ‘flat’ with
respect to the parameters, so that the maximum is
insensitive to the parameter values; - estimating the wrong model, including having too
many parameters (the best model may be simpler
than you think).
Family Members
Here aresomeof the other members of the GARCH
family. New ones are being added all the time, they are
breeding like rabbits. In these models the ‘shocks’ can
typically either have a normal distribution, a Student’s
t-distribution or a Generalized Error distribution, the
latter two having the fatter tails.
NGARCH
vn=(1−α−β)w 0 +βvn− 1 +α(
Rn− 1 −γ√
vn− 1) 2
.This is similar to GARCH(1, 1) but the parameterγ
permits correlation between the stock and volatility
processes.
AGARCH Absolute value GARCH. Similar to GARCH but
with the volatility (not the variance) being linear in the
absolute value of returns (instead of square of returns).
EGARCH Exponential GARCH. This models the logarithm
of the variance. The model also accommodates asym-
metry in that negative shocks can have a bigger impact
on volatility than positive shocks.