Timeweighted

TimeWeighted is a general weighting approach used in statistics and data analysis to assign weights to observations based on time-related factors, such as the duration between observations or the recency of data points. It aims to reflect the influence of data points more accurately when samples are irregularly spaced or when more recent measurements should carry greater importance. Time weighting contrasts with equal weighting by incorporating temporal information into the aggregation of values.

There are two common variants. Time-proportional weighting assigns weights proportional to the time interval between consecutive observations: w_i = t_i - t_{i-1}. The weighted mean is then calculated as sum(w_i * x_i) / sum(w_i). Exponential time weighting, or recency decay, assigns weights that decay with elapsed time, often w_i proportional to exp(-delta t / tau), where tau is a chosen time constant. The weighted mean in this case is also sum(w_i * x_i) / sum(w_i). The choice between variants depends on the application and how strongly recent observations should influence the result.

Applications of TimeWeighted span multiple domains. In finance, time weighting helps combine irregular cash flows into performance metrics that are not biased by the timing of deposits or withdrawals. In data science and engineering, time-weighted averages are used for irregularly sampled sensor data, where longer intervals should contribute more to the summary statistic. In reliability and quality analytics, time weighting can improve estimates that depend on the duration of exposure or measurement intervals.

Implementation considerations include ensuring accurate timestamps, selecting an appropriate weighting scheme, and performing sensitivity analyses. TimeWeighted provides a flexible framework for aggregating temporal data while accounting for uneven sampling and time-related effects.