Cascade systems de-noising and greedy calibrated approximation

Research output: Contribution to journalArticlepeer-review

Abstract

In the field of econophysics we show how stock index return volatility processes may be cast within cascade dynamics systems and investigated by greedy approximation algorithms that run on wavelet-based atomic dictionaries. The rationale behind an approach based on wavelets is that one may want to look at financial returns and corresponding volatility patterns in a transformed space where the conditional transition dynamics vary across time scales. This scale dependent information refers to market activity inherent to various time-aggregated trading horizons; thus, a variable degree of sparsity is accounted for when representing the signal, depending on the different frequency and noiseness levels. In other words, the multi-scale sequences present sparsity levels which emphasizes in some cases just a few relevant coefficients, thus letting most values be only negligibly different from pure noise. We show how this sequence space can be decomposed so as to reduce the dimensionality involved and limit the correlation effects inherited by redundant approximation dictionaries.

Original languageEnglish (US)
Pages (from-to)429-442
Number of pages14
JournalJournal of Interdisciplinary Mathematics
Volume11
Issue number3
DOIs
StatePublished - 2008
Externally publishedYes

Keywords

  • Best basis selection
  • Cascade dynamics
  • De-noising
  • Greedy approximation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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