at the figure ,you can see trying clusters of higher variance, i.e. volatility , changing with intervals of lower variance . the similarity of neighbouring variance is one more indicator for conditional heteroscedasticity . on the base of knowing the variance at time t(i.e. conditionally) you can forecast the variance at timet+1
xi. AR(1) model on the base of the AR(8) model
because of the latter analytical it would be worthwhile to estimate an AR(1) model then the condition variance of the error et is
where practically ht2 is estimate by et2
in the software used this is special case of the more general GARCH model . an ARVH(1) there corresponds to a GARCH(0,1) model . we assume here the series to follow an AR(8)
process as estimate earlier without ARTH