Nowadays, servers register more and more log entries. Monitoring, analyzing and exctracting knowledge from networks and web servers is crucial for a lot of applications. Indeed, logs can be useful for describing the activity by means of several dimensions. But logs arrive at an intensive rate and are observable at a low level of granularity which make it unrealistic to store the whole log history and leads us considering logs as data stream. Moreover, as logs are composed by several fields which can be considered as multiple levels of granularity, it would be interresting to provide an on-line analytical processing on such data stream. So, a natural question is ``is it possible to perform a multi-level and multidimensional analysis by building a cube supplied by a data stream?''. A choice has to be done in order selecting the most useful information. We tackle this problem by exploiting user's preferences. Generaly, users consult the recent history at fine levels of granularity. Then, this need of precision decreases when the age of the data increases. To this end, we introduce precision functions. Their combination lead to a compact data cube framework which can answer to most of queries. Experiments conduced on both synthetic and real data sets show that our approach can be applied to data stream context.