Dimensionality reduction and greedy learning of convoluted stochastic dynamics

Research output: Contribution to journalArticlepeer-review

Abstract

Complex natural systems may present interaction dynamics among random variables whose stochastic laws are in part or completely unknown. Statistical inference techniques applied to study such complex systems often require building suitable models that approximately describe the latent stochastic dynamics. When the observability of the variables of interest is limited by the convolution of such dynamics and noise, deconvolution techniques are needed either to estimate statistical characteristics or to decompose mixed signals. A good application field is offered by speculative financial market and their volatility stochastic dynamics. Typically, return generating stochastic processes show nonlinear, multiscale and non-stationary dynamics, especially when observed at very high frequencies. We explore the performance of computational techniques that combine the nonlinear approximation power of wavelets and associated structures with the ability of greedy learning algorithms to recover latent volatility structure by iteratively reducing the signal search space dimensionality across the most informative scales.

Original languageEnglish (US)
Pages (from-to)1928-1941
Number of pages14
JournalNonlinear Analysis: Real World Applications
Volume9
Issue number5
DOIs
StatePublished - Dec 2008
Externally publishedYes

Keywords

  • Dimensionality reduction
  • Greedy learning
  • Nonlinear approximation
  • Vaguelettes and ICA
  • Volatility deconvolution and recovery
  • Wavelets

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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