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Title: Modeling high-frequency trading volume Authors:  Eduardo Rossi - University of Pavia (Italy) [presenting]
Paolo Santucci de Magistris - LUISS Guido Carli (Italy)
Leopoldo Catania - Aarhus BBS (Denmark)
Abstract: Trading volume can be measured instantaneously for each trade or cumulated for a given time interval (time aggregates). The latter implies that for longer time intervals the trading volume is an increasing process. In high-frequency trading, this data seem to be preferred to tick-by-tick level data as it dispenses with certain pitfalls in econometric modeling, such as the irregular spacing of time spells. For short time intervals and less liquid stocks cumulated trading volume series contain a high proportion of zero observations. Further, the cumulated trading volumes series show overdispersion and intraday periodicities. Since we do not apply any transformation to the cumulated trading volumes, these have to be treated as realizations of non-negative integer random variables. When we consider long time span, cumulated trading volumes series can be characterized by trends and heterogeneity across time. The aim is to propose a new approach to the modeling of cumulated trading volumes series based on mixtures of discrete time integer-valued processes. The resulting process has a closed-form conditional density which can also be specified with time-varying parameters to accommodate the evolving features of the observed series.