Extrapolationsunsicherheiten

Extrapolation is the process of estimating unknown values that fall outside the range of observed data by extending a pattern inferred from existing data. It differs from interpolation, which estimates values within the observed range. Extrapolation relies on assumptions that the observed trend will continue beyond the available data, and it is most reliable when the underlying process is stable.

Common methods include linear extrapolation, which extends a straight line; polynomial and exponential extrapolation, which fit curves to data; and more sophisticated time-series approaches such as ARIMA or state-space models. Regression-based methods, splines, and machine learning models can also be used to project beyond the sample, often with uncertainty bounds.

Applications span science, economics, engineering, and public policy. Examples include projecting population growth, climate variable trends, demand forecasting, and risk assessment. Extrapolation is frequently employed when data are limited or when rapid preliminary estimates are needed, though it is most informative when combined with domain knowledge and uncertainty quantification.

Limitations and risks accompany extrapolation. Predictions beyond the observed range come with increasing uncertainty and can be highly sensitive to the chosen model and its assumptions. Nonstationarity, regime shifts, structural breaks, and unforeseen factors can invalidate extrapolations. Validation and transparent reporting of uncertainty are essential, including prediction intervals and, when possible, backtesting.

Historical context: Extrapolation has long been used in statistics and mathematics as a tool for extending known trends. Modern practice increasingly integrates time-series analysis, econometrics, and machine learning to better quantify uncertainty and manage risk in forecasts.