Forecasting the volatility of a financial index by wavelet transform and evolutionary algorithm

The daily volatility is a crucial variable in the study of financial risks. Traditional financial engineering methods based on parametric models such as the GARCH family, have limited success in volatility forecasting due to their rigid and linear structure. In the current paper, the integrated volatility of the 1998-2002 S&P100 index has been calculated and wavelet transformed to find the time horizon(s) that suits the subsequent forecasting procedure. In a genetic algorithm (GA) process, a group of rules based on predetermined format is trained to extract patterns from the time series. Those rules are tested to predict the 2003 S&P100 series. With 100 simple ´IF/THEN´ rules on a 4-lag recursive memory, the forecasting accuracy is shown to average 75%, matching the level achieved in other proprietary research and far superior to that of GARCH models.