| Extrapolation |
Extrapolation of Time Series and Cross-Sectional Data, J. Scott Armstrong, Wharton School, University of Pennsylvania. Below the abstract are located:
Summary of Principles for Extrapolation |
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.
- In 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.
Keywords: 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.
Summary of Principles for Extrapolation
Extrapolation consists of many simple elements, which combined into an overall process can seem complex. Here is a summary of the principles:
- To select and prepare data,
- Obtain data that represent the forecast situation;
- Use all relevant data, especially for long-term forecasts;
- Structure the problem to use the forecaster’s domain knowledge;
- Clean the data to reduce measurement error;
- Adjust intermittent data; and
- Adjust data for historical events.
- To make seasonal adjustments,
- Use seasonal adjustments if domain knowledge suggests the existence of seasonal fluctuations and if there is significant data;
- Use multiplicative factors for stable situations where there are accurate ratio-scaled data; and
- Damp seasonal factors when there is uncertainty.
- To make extrapolations,
- Combine estimates of the level;
- Use a simple estimate of trend unless there is strong evidence to the contrary;
- Weight the most recent data more heavily than earlier data when measurement errors are small, forecast horizons are short, and the series is stable;
- Be conservative when the situation is uncertain;
- Use domain knowledge to provide pre-specified adjustments to extrapolations;
- Use statistical procedures as an aid in selecting an extrapolation method;
- Update estimates of model parameters frequently; and
- Use cycles only when the evidence on future timing and amplitude is highly accurate.
- To assess uncertainty,
- Use empirical estimates drawn from out-of-sample tests.
- For ratio-scaled data, estimate prediction intervals by using log transforms of the actual and predicted values; and
- Add safety factors for contrary series.
- Use extrapolations when,
- A large number of forecasts is needed;
- The forecaster is ignorant about the situation;
- The situation is stable;
- Other methods would be subject to forecaster bias; and
- A benchmark forecast is needed to assess the effects of policy changes.
Progress in extrapolation will depend on success in integrating judgment. In addition, systematic procedures are needed to incorporate cumulative knowledge. Software programs can play an important role here.
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