US Patent 11164092 Parallel time series analysis

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for parallel time series analysis. One of the methods includes receiving a plurality of data elements. The plurality of data elements are partitioned into a plurality of chunks, wherein the plurality of chunks, including a first chunk and a plurality of additional chunks, have an ordering according to the data elements included in each chunk. Each chunk is assigned to a particular segment of a plurality of segments. A first iteration of an autoregressive integrated moving average is computed for each chunk assigned to each segment. A second iteration of the autoregressive integrated moving average is computed for each chunk assigned to each segment, wherein computing uses the result data for a corresponding preceding chunk in the first iteration. One or more additional iterations of the autoregressive integrated moving average are computed until stopping criteria has been satisfied.