Extrapolarea

Extrapolarea, the Romanian term for extrapolation, is the process of estimating values beyond the range of observed data by extending a known pattern or model. It relies on the assumption that the identified relationship continues outside the available data, allowing forecasts or inferences about unobserved quantities. Extrapolation is used across disciplines, including statistics, economics, physics, engineering, and environmental science, to project future values or to infer conditions outside recorded measurements.

Common methods include linear extrapolation from a linear trend, polynomial extrapolation based on fitted polynomials, and extrapolation that assumes exponential or logarithmic growth or decay. Regression-based approaches and time-series forecasting models (such as ARIMA or related techniques) are frequently employed to predict values beyond the observed horizon. In machine learning contexts, more complex models can attempt to generalize to unseen regions of the input space, albeit with increased risk.

Extrapolation is distinct from interpolation, which estimates values within the known data range. It carries higher uncertainty because it extends beyond validated territory. Reliability depends on model validity, data quality, and the stability of the underlying relationships. Structural breaks, regime changes, nonstationarity, or incorrect model specification can lead to biased or implausible predictions. Practitioners often accompany extrapolated estimates with uncertainty quantification, sensitivity analyses, and scenario testing.

See also: Interpolation, Forecasting, Time series, Regression.