Principles of Forecasting

Volume 30 of the series International Series in Operations Research & Management Science pp 217-243

Extrapolation for Time-Series and Cross-Sectional Data

  • J. Scott ArmstrongAffiliated withThe Wharton School, University of Pennsylvania

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Extrapolation methods are reliable, objective, inexpensive, quick, and easily automated. As a result, they are widely used, especially for inventory and production forecasts, for operational planning for up to two years ahead, and for long-term forecasts in some situations, such as population forecasting. This paper provides principles for selecting and preparing data, making seasonal adjustments, extrapolating, assessing uncertainty, and identifying when to use extrapolation. The principles are based on received wisdom (i.e., experts’ commonly held opinions) and on empirical studies. Some of the more important principles are:
  • In selecting and preparing data, use all relevant data and adjust the data for important events that occurred in the past.

  • Make seasonal adjustments only when seasonal effects are expected and only if there is good evidence by which to measure them.

  • When extrapolating, use simple functional forms. Weight the most recent data heavily if there are small measurement errors, stable series, and short forecast horizons. Domain knowledge and forecasting expertise can help to select effective extrapolation procedures. When there is uncertainty, be conservative in forecasting trends. Update extrapolation models as new data are received.

  • To assess uncertainty, make empirical estimates to establish prediction intervals.

  • Use pure extrapolation when many forecasts are required, little is known about the situation, the situation is stable, and expert forecasts might be biased.


Acceleration adaptive parameters analogous data asymmetric errors base rate Box-Jenkins Combining Conservatism contrary series cycles damping decomposition discontinuities domain knowledge experimentation exponential smoothing functional form judgmental adjustments M-Competition measurement error moving averages nowcasting prediction intervals projections random walk seasonality simplicity tracking signals trends uncertainty updating