Abstract: Embodiments for efficiently computing complex statistics from historical time series data are provided. A hierarchical summarization method includes receiving at least one stream of data and creating data blocks from the at least one stream of data. In another embodiment, a method for computing statistics for historical data includes accessing at least one online stream of historical data, the online stream of historical data including metadata, and creating data blocks from the at least one online stream of historical data. Each data block includes a pair of timestamps indicating a sampling start time and a sampling end time, a number of data samples spanned by the data block, a SUM(X) statistic, a SUM(XX) statistic, and a SUM(XY) statistic computed for the data samples spanned by the data block. Other methods are also presented, such as methods for efficiently and accurately calculating statistical queries regarding historical data for arbitrary time ranges, among others.