FUNCTIONAL APPROXIMATION IN MULTISCALE COMPLEX SYSTEMS

One common approach for exploring, approximating and estimating complex system dynamics refers to models based on elementary or atomic building block components of easier interpretation and efficient computation. We adopt a combination of wavelets, greedy approximation and subspace techniques to investigate complex systems such as speculative financial markets. These systems are endowed with multiscale and non-stationary dynamics that we aim to artificially learn by using functional approximation and optimization theory. We show that volatility dynamics are embedded in a sequence of nested informative scales and thus a multiscale estimation approach is indicated to deal with them.