GARCH and Neural Network Models for Volatility Prediction for the USA Stock Market

In the course of the work, GARCH, EGARCH, and GJR GARCH models were considered and studied, taking into account the asymmetry and heavy tails of distributions for financial indicators, represented by the index S & P 500. With the help of Akaike information criterion and various types of errors, it was shown that the model EGARCH-t (1,1) describes the volatility on this index most accurately. The study showed the inconsistency of models with a normal distribution - GARCH (1,1) and GJR (1,1). Models for both indexes had a significant excess of market risk at a confidence level of 99%. Also, according to information criteria, the use of the skewed t-distribution of the Student gives the best result. This distribution allows us to take into account the known effect of leptokurtosis of financial data and provides an additional improvement in the result. However, when choosing a model, it is necessary to monitor, so that values of the distribution parameters and the specification of the model as a whole are significant.