Computing aggregation over sliding windows, i.e., finite subsets of an unbounded stream, is a core operation in streaming analytics. We propose PBA (Parallel Boundary Aggregator), a novel parallel algorithm that groups continuous slices of streaming values into chunks and exploits two buffers, cumulative slice aggregations and left cumulative slice aggregations, to compute sliding window aggregations efficiently. PBA runs in (1) time, performing at most 3 merging operations per slide while consuming () space for windows with partial aggregations. Our empirical experiments demonstrate that PBA can improve throughput up to 4× while reducing latency, compared to state-of-the-art algorithms.