  In this paper we study the high frequency dynamic of financial volumes of
traded stocks by using a semi-Markov approach. More precisely we assume that
the intraday logarithmic change of volume is described by a weighted-indexed
semi-Markov chain model. Based on this assumptions we show that this model is
able to reproduce several empirical facts about volume evolution like time
series dependence, intra-daily periodicity and volume asymmetry. Results have
been obtained from a real data application to high frequency data from the
Italian stock market from first of January 2007 until end of December 2010.
