Dimension reduction and multi-scaling law through source extraction

Research output: Contribution to journalConference articlepeer-review

Abstract

Through the empirical analysis of financial return generating processes one may find features that are common to other research fields, such as internet data from network traffic, physiological studies about human heart beat, speech and sleep recorded time series, geophysics signals, just to mention well-known cases of study. In particular, long range dependence, intermittency, heteroscedasticity are clearly appearing, and consequently power laws and multi-scaling behavior result typical signatures of either the spectral or the time correlation diagnostics. We study these features and the dynamics underlying financial volatility, which can respectively detected and inferred from high frequency realizations of stock index returns, and show that they vary according to the resolution levels used for both the analysis and the synthesis of the available information. Discovering whether the volatility dynamics are subject to changes in scaling regimes requires the consideration of a model embedding scale-dependent information packets, thus accounting for possible heterogeneous activity occurring in financial markets. Independent component analysis result to be an important tool for reducing the dimension of the problem and calibrating greedy approximation techniques aimed to learn the structure of the underlying volatility.

Original languageEnglish (US)
Pages (from-to)360-370
Number of pages11
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume5102
DOIs
StatePublished - 2003
Externally publishedYes
EventIndependent Component Analyses, Wavelets, And Neural Networks - Orlando, FL, United States
Duration: Apr 22 2003Apr 25 2003

Keywords

  • Atomic decompositions
  • Dimension reduction
  • Greedy approximation
  • Independent component analysis
  • Volatility scaling regimes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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