Empirical volatility analysis: feature detection and signal extraction with function dictionaries

We aim to investigate the potential usefulness of wavelets for representing and decomposing financial volatility processes. Our strategy relies on the empirical analysis of high-frequency intradaily stock index returns by using adaptive signal-processing techniques which exploit the approximation and computational power of wavelet transforms. We first deal with data pre-processing and pre-smoothing, before addressing the statistical model building stage. We thus introduce a flexible parametric model that yields an effective empirical volatility analysis tool, capable of handling and detecting latent periodicities, and consequently delivering more accurate signal estimates. We extract the structure of volatility through the information content of projected signals obtained by representing and approximating the observed returns with special function dictionaries that may significantly contribute to reduce the risk that standard volatility models might fail to achieve meaningful statistical inference.