A significant line of work deals with processing data stream to produce key performance indicators as temporal aggregates. Nowadays, stream systems handle events with a lifespan, such as phone calls, as points in time. They also mainly assume streams with no delay. Both spanning events and out-of-order events undoubtedly yield to noisy aggregates. In this communication, we develop an engine for Aggregate Continuous Query (ACQ), which is able to (i)~incorporate lifespan to provide exact aggregate computation, (ii)~properly manage out-of-order events, and (iii)~follow a cost-based policy that allows elaborating at run-time the most efficient query execution plan of multiple ACQs. The query engine is supported by data structures dedicated to spanning and out-order events and a hybrid sharing schema that aggressively saves computation cost among multiple queries. A lot of experiments have been conducted to show the efficiency of the approach in a large variety of settings and stream profiles.