Much of the research regarding streaming data has focused only on real time querying and analysis of recent data stream allowable in memory. However, as data stream mining, or tracking of past data streams, is often required, it becomes necessary to store large volumes of streaming data in stable storage. Moreover, as stable storage has restricted capacity, past data stream must be summarized. The summarization must be performed periodically because streaming data flows continuously, quickly, and endlessly. Therefore, in this paper, we propose an efficient periodic summarization method with a flexible storage allocation. It improves the overall estimation error by flexibly adjusting the size of the summarized data of each local time section. Additionally, as the processing overhead of compression and the disk I/O cost of decompression can be an important factor for quick summarization, we also consider setting the proper size of data stream to be summarized at a time. Some experimental results with artificial data sets as well as real life data show that our flexible approach is more efficient than the existing fixed approach.