Transaction-time temporal databases and query languages provide a solid framework for analyzing properties of queries over data streams. In this paper we focus on issues connected with the construction of space-bounded synopses that enable answering of continuous queries over unbounded data streams while requiring only limited space. We link the problem to the problem of query-driven data expiration in append-only temporal databases and study space bounds on synopses that are sufficient and necessary for query answering under duplicate semantics.