rundifference

Rundifference is a term used in some data analysis and time-series contexts to describe the incremental change observed in a quantity that is updated in a running fashion as new data arrive. It is closely related to the idea of a first difference but is applied specifically to quantities that are computed cumulatively or iteratively, such as running sums, running means, or other evolving statistics.

Formal concept

If S_t denotes a running statistic updated with the t-th observation x_t, then the rundifference at time t is D_t = S_t − S_{t−1}. This captures how much the statistic changes due to the latest data point. The exact value of D_t depends on the update rule for S_t. For a simple running sum S_t = ∑_{i=1}^t x_i, the rundifference D_t equals x_t. For other running statistics, such as a running mean, D_t reflects both the new observation and the changing weight of past data.

Applications

Rundifference is used conceptually to monitor momentum or shifts in streaming data, including change detection and anomaly monitoring. By examining D_t, analysts can identify abrupt increases or decreases in the evolving statistic, separate from fluctuations in the raw data.

Relation to other concepts

Rundifference is a specialized form of the broader first-difference operator and is related to delta measures in time-series analysis. It emphasizes the impact of new observations on a running quantity rather than on the raw data alone.

Notes

The term is not universally standardized and may be used variably across disciplines. When encountered, it is typically described in relation to a specific running statistic and its update mechanism.