Modeling Volatility with GARCH Class Models

In Chapter 6, Time Series Analysis and Forecasting, we looked at various approaches to modeling time series. However, models such as ARIMA (Autoregressive Integrated Moving Average) cannot account for volatility that is not constant over time (heteroskedastic). We have already explained that some transformations (such as log or Box-Cox transformations) can be used to adjust for modest changes in volatility, but we would like to go a step further and model it.

In this chapter, we focus on conditional heteroskedasticity, which is a phenomenon caused when an increase in volatility is correlated with a further increase in volatility. An example might help to understand this concept. Imagine the price of an asset going down significantly due to some breaking news related to the company. Such a sudden price drop could trigger certain risk management tools of investment funds, which start selling the stocks as a result of the previous decrease...