Multiresolution Properties of Volatility Models
by
Enrico Capobianco
CNR, Research Associate

We report on the multiresolution analysis of high frequency intradaily stock return indices by using signal processing techniques based on wavelets. Wavelets represent a novelty too as far as applications in finance are concerned, and one goal is thus to show their potential usefulness in the field. In particular, we use wavelet transforms and algorithms for pre-processing the observed data so to de-noise returns before setting up models for interpreting them.

In this way we try to discover latent structure in the stochastic processes underlying the observed data.

We show that the task of detecting hidden features is greatly improved by the use of such methodologies; we make short and long run dependences together with stochastic periodicities more evident and thus by removing them we suggest how to model and fit the data according to standard volatility techniques.

The risk of ignoring or just overlooking these aspects may lead to a misleading or meaningless statistical inference analysis.

Key Words: Intraday Stock Returns; Wavelet Decomposition; Data De-noising; Multiresolution; Matching Pursuit Algorithm.

(P)

Date received: April 12, 2000