A new approach for handling stream imperfections based on speculative execution involves the retraction of incorrect events facilitated using operators to remove speculatively produced incorrect output. Additionally, parameters are disclosed that define a spectrum of consistency levels. A first parameter, maximum blocking time, exposes a tradeoff between a degree of speculation and latency. A second parameter, the maximum time data is remembered before being purged from the system, exposes a tradeoff between state size and correctness. Varying these two parameters produces a spectrum of consistency levels (e.g., strong, middle, weak) which address the specific tradeoffs built into other systems. Retraction is accomplished using operators that include Select, AlterLifetime, Join, Sum, Align, and Finalize.