The specifications of various domains include properties which persist, at the latest, by some future time. In multi-agent voting protocols, e.g., a proposed motion may be seconded at the latest by some specified time. Contemporary applications additionally require efficient temporal pattern matching over high-velocity streams, for computing the values of such properties with minimal latency. To address these issues, we present a formal computational framework, based on the Event Calculus, that handles effectively streams including events with temporally-constrained effects. We present the syntax, semantics, reasoning algorithms and complexity of our proposed framework. Furthermore, we present an empirical analysis on large synthetic and real data streams.