The GARCH model
Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) is an important extension of ARCH, by Bollerslev (1986). The GARCH (p,q) process is defined as follows:
Here, 
is the variance at time t, q is the order for the error terms, p is the order for the variance, 
is a constant, 
is the coefficient for the error term at t-i, 
is the coefficient for the variance at time t-i. Obviously, the simplest GARCH process is when both p and q are set to 1, that is, GARCH (1,1), which has following formula:
