Dimensionality reduction and greedy learning of convoluted stochastic dynamics

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.