This paper presents advanced data compression techniques for predicting stock markets behavior under widely accepted market models in finance. Our techniques are applicable to technical analysis, portfolio theory, and nonlinear market models. We find that lossy and lossless compression techniques are well suited for predicting stock prices as well as market modes such as strong trends and major adjustments. We also present novel applications of multispectral compression techniques to portfolio theory, correlation of similar stocks, effects of interest rates, transaction costs and taxes.