Kernel methods and flexible inference for complex stochastic dynamics

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Approximation theory suggests that series expansions and projections represent standard tools for random process applications from both numerical and statistical standpoints. Such instruments emphasize the role of both sparsity and smoothness for compression purposes, the decorrelation power achieved in the expansion coefficients space compared to the signal space, and the reproducing kernel property when some special conditions are met. We consider these three aspects central to the discussion in this paper, and attempt to analyze the characteristics of some known approximation instruments employed in a complex application domain such as financial market time series. Volatility models are often built ad hoc, parametrically and through very sophisticated methodologies. But they can hardly deal with stochastic processes with regard to non-Gaussianity, covariance non-stationarity or complex dependence without paying a big price in terms of either model mis-specification or computational efficiency. It is thus a good idea to look at other more flexible inference tools; hence the strategy of combining greedy approximation and space dimensionality reduction techniques, which are less dependent on distributional assumptions and more targeted to achieve computationally efficient performances. Advantages and limitations of their use will be evaluated by looking at algorithmic and model building strategies, and by reporting statistical diagnostics.

Original languageEnglish (US)
Pages (from-to)4077-4098
Number of pages22
JournalPhysica A: Statistical Mechanics and its Applications
Volume387
Issue number16-17
DOIs
StatePublished - Jul 1 2008
Externally publishedYes

Keywords

  • Frames
  • Overcomplete atomic dictionaries
  • Reproducing Kernel Hilbert spaces
  • Sparse approximation
  • Wavelets

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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