ABSTRACT
This chapter considers various classes of non-linear models of a completely different type, which are primarily concerned with modelling changes in variance or volatility. Volatility models have many applications in economics and finance. In risk management, volatility models provide a simple approach to calculating the value at risk of a financial position. The basic idea in volatility modeling is that the return series has very few serial correlations, but it is a dependent series. Volatility also plays an important role in asset allocation and portfolio optimization. Historic volatility uses equal weights for the observations in the moving window of returns. Similar to autoregressive conditional heteroskedastic (ARCH) models, generalised ARCH models do not affect point forecasts of the original observed variable, and it is therefore rather difficult to make a fair comparison of the forecasting abilities of different models for changing variance.
