Abstract: By systematically applying different engineering
methods, difficult financial problems become approachable. Using a
combination of theory and techniques such as wavelet transform,
time series data mining, Markov chain based discrete stochastic
optimization, and evolutionary algorithms, this work formulated a
strategy to characterize and forecast non-linear time series. It
attempted to extract typical features from the volatility data sets of
S&P100 and S&P500 indices that include abrupt drops, jumps and
other non-linearity. As a result, accuracy of forecasting has reached
an average of over 75% surpassing any other publicly available
results on the forecast of any financial index.