Zeitgewichtete

Zeitgewichtete, literally “time-weighted” in German, refers to a weighting approach where the duration that a value or observation applies influences its influence on a computed statistic. The concept is used in statistics, data analysis, and finance to reflect the temporal persistence of values.

In statistics, a zeitgewichtete (time-weighted) mean assigns more influence to values that last longer within the observation window. If a value x_i remains constant for a time interval Δt_i, the time-weighted average over a horizon T is the sum of x_i Δt_i divided by T. For continuous data, the time-weighted average can be expressed with an integral: (1/T) ∫ x(t) dt. This approach contrasts with simple averages that treat all observations equally regardless of duration.

In finance, time-weighted return (zeitgewichtete Rendite) measures investment performance independently of cash flows. The period is divided into subperiods by cash flows, and returns within each subperiod are chained together: (1+r1)(1+r2)…(1+rn) − 1. This method isolates the performance of the asset manager from the effects of deposits or withdrawals, and it is often contrasted with money-weighted returns (internal rate of return).

Applications include performance evaluation of portfolios, environmental and quality monitoring, and process control. Limitations involve the need for precise timing data and potential misinterpretation if users expect metrics that reflect capital inflows or outflows. Related concepts include weighted averages and money-weighted returns.