Ten lectures on wavelets
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
A fast fixed-point algorithm for independent component analysis
Neural Computation
Atomic Decomposition by Basis Pursuit
SIAM Review
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
Learning Overcomplete Representations
Neural Computation
Fast and robust fixed-point algorithms for independent component analysis
IEEE Transactions on Neural Networks
Preface: Second Special issue on Computational Econometrics
Computational Statistics & Data Analysis
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I present a statistical model to allow inferences about a volatility process that does not rely on parametric assumptions and uses algorithms that decompose the observed signals with overcomplete dictionaries of functions. By combining multiresolution approximation and Independent Component analysis, we increase the detection power of important volatility features in non-stationary latent variable systems. The computational learning machine is based on the Matching Pursuit algorithm, whose performance is monitored through the residual sequence used to extract information about the volatility structure. I employ wavelet packets because they have high localization power and represent overcomplete dictionaries. Beyond improved characterization of the volatility process, the proposed methods achieve a near-optimal trade-off between both time-and frequency-resolution pursuit.