Independent multiresolution component analysis and matching pursuit

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 over-complete 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. (C) 2002 Elsevier Science B.V. All rights reserved.