Forecasting volatility using GARCH models
In the previous recipes, we have seen how to fit ARCH/GARCH models to a return series. However, the most interesting/relevant case of using ARCH class models would be to forecast the future values of the volatility.
There are three approaches to forecasting volatility using GARCH class models:
- Analytical – due to the inherent structure of ARCH class models, analytical forecasts are always available for the 1-step ahead forecast. Multi-step analytical forecasts can be obtained using a forward recursion, however, that is only possible for models which are linear in the square of the residuals (such as GARCH or Heterogeneous ARCH).
- Simulation – simulation-based forecasts use the structure of an ARCH class model to forward simulate possible volatility paths using the assumed distribution of residuals. In other words, they use random number generators (assuming specific distributions) to draw the standardized residuals. This approach...
