1. At a computing system comprising one or more computing devices and one or more storage media, each of the one or more computing devices comprising one or more processors, a computing-system-implemented method for generating an autocorrelation for data elements in an adjusted computation window, the method comprising: initializing, by the computing-device-based computing system, a lag l (l>0), a computation window size n (n>2*l+1), a sum or a mean or both, and one or more other components of an autocorrelation at lag l for a computation window with size n of a buffer on at least one of the one or more storage media; accessing or receiving, by the computing-device-based computing system, a data element or information about a data element to be removed from the computation window; removing, by the computing-device-based computing system, the to-be-removed data element from the buffer; adjusting, by the computing-device-based computing system, the computation window by: removing the to-be-removed data element from the computation window; and adjusting the computation window size; decrementally deriving, by the computing-device-based computing system, a sum or a mean or both for the adjusted computation window; directly decrementally deriving, by the computing-device-based computing system and based at least in part on the one or more components of the autocorrelation at lag l other than a sum and a mean for the computation window, one or more components of an autocorrelation at lag l other than a sum and a mean for the adjusted computation window, including: accessing l data elements from each side of the adjusted computation window respectively and the removed data element whereby not all data elements in the adjusted computation window are accessed to reduce data access latency thereby saving computing resources and reducing the computing system's power consumption; accessing each of the one or more components of the autocorrelation at lag l other than a sum and a mean for the computation window; removing any contribution of the removed data element from each of the accessed components mathematically based on the removed data element and/or the l data elements from each side of the adjusted computation window wherein not all data elements in the adjusted computation window are used during the directly decrementally deriving the one or more components of the autocorrelation to reduce the number of operations performed by the computing system, thereby increasing calculation efficiency; generating, by the computing-device-based computing system, an autocorrelation at lag l for the adjusted computation window based on one or more of the decrementally calculated components.