extrapolaation

Extrapolation is the process of estimating unknown values that lie outside the range of observed data by using a model fitted to existing data. In statistics, it is often contrasted with interpolation, which estimates values within the range of the observed data. Extrapolation assumes that the pattern or relationship identified within the data continues beyond the observed domain. Because the further the forecast is from known data, the greater the risk, extrapolated estimates typically come with higher uncertainty than interpolated ones.

Common methods include simple linear extrapolation, where a straight line is extended beyond the data; polynomial and spline extrapolation, where fitted curves extend beyond the domain; and model-based extrapolation using regression, exponential or logistic growth models. In time series analysis, forecasting techniques such as ARIMA, exponential smoothing, or state-space models are routinely used to project future values. The choice of model and the validity of its underlying assumptions critically affect the plausibility of the extrapolated results.

Uncertainty is inherent in extrapolation. Analysts quantify it with prediction or projection intervals, and they test robustness by examining alternative models and scenarios. It is essential to consider domain knowledge, data quality, and potential regime changes that may alter the relationship beyond the observed range. Extrapolation is widely used in science, finance, and engineering to forecast trends, assess risks, and guide policy, but conclusions drawn from extrapolated values should be treated as conditional on the assumed continuity of patterns and the chosen model.