Waiting time distributions of the volatility in the Italian MIB30 index: Clustering or Poisson functions?

We investigate the time behaviour of the Italian MIB30 stock index collected every minute during two months in the period from May 17, 2006, up to July 24, 2006. We find short-range correlations in the price returns and, on the contrary, a long persistent time lag and slow decay in the autocorrelation functions of volatility. Besides, we find that the probability density functions (PDFs) of returns show fat tails, which are well fit by the log-normal model of Castaing [B. Castaing, Y. Gagne, E.J. Hopfinger, Physica D 46 (1990) 177], and a convergence toward a normal distribution for large time scales; we also find that the PDFs of volatility, for short time horizons, fit better with a log-normal distribution than with a Gaussian. Most of these features characterize the indexes and stocks of the largest American, European and Asian markets.