A recent trend in data stream processing shows the use of advanced continuous queries (CQs) that reference non-streaming resources such as relational data in databases and machine learning models. Since non-streaming resources could be shared among multiple systems, resources may be updated by the systems during the CQ execution. As a consequence, CQs may reference resources inconsistently, and lead to a wide range of problems from inappropriate results to fatal system failures. We address this inconsistency problem by introducing the concept of transaction processing onto data stream processing. We introduce CQ-derived transaction, a concept that derives read-only transactions from CQs, and illustrate that the inconsistency problem is solved by ensuring serializability of derived transactions and resource updating transactions. To ensure serializability, we propose three CQ-processing strategies based on concurrency control techniques: two-phase lock strategy, snapshot strategy, and optimistic strategy. Experimental study shows our CQ-processing strategies guarantee proper results, and their performances are comparable to the performance of conventional strategy that could produce improper results.