The document generally describes hardware for computing multiple orders of statistical moments. In one aspect, a system includes multiple stages of compute units. A first stage includes a first sequence of compute units includes a first compute unit configured to compute a first raw statistical moment for a first portion of data points in the time series of data points and one or more first additional compute units that are each configured to compute a respective first statistical moment for the first portion of data points. Each additional stage includes a second sequence of compute units for computing statistical moments for a respective second portion of the time series of data points. Each additional stage includes a second compute unit configured to compute the first raw statistical moment for the respective second portion of the time series of data points and one or more second additional compute units.