The Innovation Distributions
The distribution of the innovations is the second most important component in a process. With a good understanding of the heteroskedasticity, the distribution of the empirical innovations can be studied. A normal distribution can be clearly rejected, regardless of the model used for the heteroskedasticity. A Student distribution with a number of degrees of freedom around 5 gives a simple and good characterization of the empirical distributions. This shows that the fat tail observed in the return distributions is mostly generated by the innovations, while the volatility feed-back mechanism plays a small role.