Stochastic decomposition and approximation of stock index return volatility

This work is about applying wavelet-based approximation and estimation techniques to non-stationary nancial time series for modeling stock index return volatility. The presence of various forms of dependence requires a careful analysis, particularly when dealing with very high frequencies and with periodic components. One important goal is achieving sparse signal decompositions, by the means of global and local function optimizers running through wavelet and cosine packet dictionaries, which are well suited for dealing with data of a complex nature. Another goal is obtaining a signal decomposition over statistically independent coordinates, so to let the algorithms learn in a more e ective way the true structure characterizing volatility processes. 2000 Mathematics Subject Classi cation: 60H30, 62M10, 62G07.