extrapolaties

Extrapolaties, commonly referred to in English as extrapolations, are estimates of values outside the range of observed data, obtained by extending a model or trend. They project patterns into regions where no data were collected, such as forecasting future values from historical series or predicting a sensor reading beyond the last measurement.

Common methods include linear extrapolation using a straight-line fit, and more complex forms such as polynomial, logarithmic, or exponential extrapolation. Time-series forecasting often relies on models like ARIMA, exponential smoothing, or machine learning approaches. The choice depends on the presumed underlying relationship and the range of extrapolation.

Extrapolation assumes the chosen model describes the true relationship beyond observed data. The farther the extrapolation from the available data, the greater the potential error, and confidence intervals may widen dramatically.

Limitations include sensitivity to structural breaks, regime shifts, nonstationarity, data quality issues, and outliers. Because extrapolated values lie outside the observed range, they should be interpreted with caution, and validation through backtesting, holdout data, or comparing multiple models is recommended.

Applications span science, climate and environmental projections, economics and finance, engineering, and epidemiology, where future trends or unknown values are needed despite limited data.

See also: interpolation, projection, forecasting, trend analysis.