High performance architectures for processing distributed data streams, such as Flink, Spark, and Storm, are increasingly deployed in emerging data-driven computing systems. Exploiting the parallelism afforded by such platforms, while preserving the semantics of the desired computation, is prone to errors, and motivates the development of tools for specification, testing, and verification. We focus on the problem of differential output testing for distributed stream processing systems, that is, checking whether two implementations produce equivalent output streams in response to a given input stream. The notion of equivalence allows reordering of logically independent data items, and the main technical contribution of the paper is an optimal online algorithm for checking this equivalence. Our testing framework is implemented as a library called \library in Flink. We present four case studies to illustrate how our framework can be used to (1) correctly identify bugs in a set of benchmark MapReduce programs, (2) facilitate the development of difficult-to-parallelize high performance applications, and (3) monitor an application for a long period of time using minimal computational resources.