RollingSum

Description

The RollingSum class computes the sum of values within a specified moving window over a sequence of data. This rolling sum provides a dynamic aggregate of values in the window as it moves across the data, enabling analysis of trends over localized segments.

Parameters:

• window_size: Specifies the size of the rolling window.

• start_policy: Defines how the function handles the initial phase when fewer than window_size data points are available. This parameter accepts one of the following three values:

  • "strict": Returns NaN for all calculations until window_size elements have been processed.

  • "expanding": Adapts the computation by dynamically reducing the window size to include all available data, starting from a single point and growing until window_size is reached.

  • "zero": Simulates a full initial window of zeros, effectively pre-filling the data stream with window_size zeros before processing the actual input.

Usage Example and Plot

Implementation Details

Algorithm

RollingSum implements cyclic buffers to accumulate windowed statistics.

Complexity

• Time Complexity: O(log(1)) per new element due to the insertion and deletion operations in the heaps.

• Space Complexity: O(window_size), as only elements within the current window are stored.