arrayCMA

arrayCMA is a data structure and algorithmic approach designed to maintain cumulative moving averages over one-dimensional data sequences. It combines array-based storage with mechanisms to compute CMAs for one or more window sizes, enabling smoothing and trend detection in time-series data.

The design typically uses a circular buffer to store the most recent values and a set of running sums for each requested window length. When a new value arrives, it is appended and, if necessary, the oldest value is removed to keep the window at its target size. Running sums are updated accordingly in constant time. Querying a CMA for a given window length is done by dividing the corresponding running sum by the window length, also in constant time. For multiple windows, several sums can be maintained concurrently. Some implementations supplement running sums with prefix sums to accelerate batch queries.

Complexity and trade-offs: updates for each tracked window are constant time, and memory usage scales with the number of active window sizes or with the length of the stored history if the full array is retained. The method is well suited to streaming data and real-time dashboards. Trade-offs include the added complexity of supporting variable-length windows and initialization effects at startup.

Applications include smoothing noisy signals, anomaly detection, financial time-series analysis, signal processing, and performance monitoring. The arrayCMA approach provides a compact, fast mechanism to derive immediate trend information from incoming data without recomputing averages from scratch.