Traffic measurement provides essential information for various network services. Burst is a common phenomenon in high-speed network streams, which manifests as a surge in the number of incoming packets in a flow. We propose a new definition named across-period burst, considering the change not in two adjacent time windows but in two groups of windows with time continuity. The across-period burst definition can better capture the continuous changes of flows in high-speed networks. To achieve real-time burst detection with high accuracy and low memory consumption, we propose a novel sketch named BurstDetector, which consists of two stages. Stage 1 excludes those flows that will not become burst flows, while Stage 2 accurately records the information of the potential burst flows and carries out across-period burst detections at the end of every time window. We further propose an optimization called Hierarchical Cell, which can improve the memory utilization of BurstDetector. In addition, we analyze the estimation accuracy and time complexity of BurstDetector. Extensive experiments based on real-world datasets show that our BurstDetector can achieve at least 2.8 times as much detection accuracy and processing throughput as some existing algorithms.