Independent Multiresolution Component Analysis and Matching Pursuit

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15 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)385-402
Number of pages18
JournalComputational Statistics and Data Analysis
Volume42
Issue number3
DOIs
StatePublished - Mar 28 2003
Externally publishedYes

Keywords

  • Feature detection
  • Financial time series
  • Independent and sparse components
  • Latent variable systems
  • Matching pursuit
  • Multiresolution analysis
  • Overcomplete dictionaries

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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