Before revision:  To demonstrate this point, we construct regions (phase diagrams) in higher order moment space, where a GARCH(1,1) model can be used to fit the higher order moments and compare this with empirical data from different sectors of the economy.
After revision:  To demonstrate this point, we construct regions (phase diagrams) in the fourth and sixth order standardised moment space, where a GARCH(1,1) model can be used to fit the higher order moments and compare this with empirical data from different sectors of the economy.