We design a predictive methodology for elastic data stream processing.We exploit Model Predictive Control to design the predictive controller.We regulate the number of used cores and the CPU frequency.The approach targets multicore-based shared-memory systems.The approach allows the design of strategies that achieve good SASO trade-offs. Data stream processing applications have a long running nature (24hr/7d) with workload conditions that may exhibit wide variations at run-time. Elasticity is the term coined to describe the capability of applications to change dynamically their resource usage in response to workload fluctuations. This paper focuses on strategies for elastic data stream processing targeting multicore systems. The key idea is to exploit Model Predictive Control, a control-theoretic method that takes into account the system behavior over a future time horizon in order to decide the best reconfiguration to execute. We design a set of energy-aware proactive strategies, optimized for throughput and latency QoS requirements, which regulate the number of used cores and the CPU frequency through the Dynamic Voltage and Frequency Scaling (DVFS) support offered by modern multicore CPUs. We evaluate our strategies in a high-frequency trading application fed by synthetic and real-world workload traces. We introduce specific properties to effectively compare different elastic approaches, and the results show that our strategies are able to achieve the best outcome.