Hammerstein system represention of financial volatility processes
CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
Corresponding author: a Enrico.Capobianco@cwi.nl
Published online: 15 May 2002
We show new modeling aspects of stock return volatility processes, by first representing them through Hammerstein Systems, and by then approximating the observed and transformed dynamics with wavelet-based atomic dictionaries. We thus propose an hybrid statistical methodology for volatility approximation and non-parametric estimation, and aim to use the information embedded in a bank of volatility sources obtained by decomposing the observed signal with multiresolution techniques. Scale dependent information refers both to market activity inherent to different temporally aggregated trading horizons, and to a variable degree of sparsity in representing the signal. A decomposition of the expansion coefficients in least dependent coordinates is then implemented through Independent Component Analysis. Based on the described steps, the features of volatility can be more effectively detected through global and greedy algorithms.
PACS: 02.50.Tt – Inference methods / 05.45.Tp – Time series analysis / 02.60.Gf – Algorithms for functional approximation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002