RollingZscore

Description

The RollingZscore class computes the rolling z-score for each value in a specified moving window, representing how many standard deviations each data point is from the mean of its window. This metric is useful for identifying outliers or deviations in a sequence.

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

RollingZscore 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.