Diffusion Entropy technique applied to the study of the market activity

The present work briefly summarizes the results obtained in Palatella et al. Eur. Phys. J. B 38 (2004) 671 using the Diffusion Entropy technique and adds some new results regarding the Dow Jones Index time series. We show that time distances between peaks of volatility or activity are distributed following an asymptotic power-law which ultimately recovers an exponential behavior. We discuss these results in comparison with the TARCH model, the Ornstein-Uhlenbeck stochastic volatility model and a multi-agent model. We conclude that both ARCH and stochastic volatility models better describe the observed experimental evidences.