# Forecast Error Metric

A Forecast Error Metric is an error metric for a forecast function.

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**Example(s):****See:**Forecast Task, Point Estimate Error, Forecast Performance Measure.

## References

### 2013

- en.wikipedia.org/wiki/Calculating_demand_forecast_accuracy
- The forecast error needs to be calculated using actual sales as a base. There are several forms of forecast error calculation methods used, namely Mean Percent Error, Root Mean Squared Error, Tracking Signal and Forecast Bias ..

- http://en.wikipedia.org/wiki/Forecast_error
- In statistics, a
**forecast error**is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest.In simple cases, a forecast is compared with an outcome at a single time-point and a summary of forecast errors is constructed over a collection of such time-points. Here the forecast may be assessed using the difference or using a proportional error. By convention, the error is defined using the value of the outcome

*minus*the value of the forecast.In other cases, a forecast may consist of predicted values over a number of lead-times; in this case an assessment of forecast error may need to consider more general ways of assessing the match between the time-profiles of the forecast and the outcome. If a main application of the forecast is to predict when certain thresholds will be crossed, one possible way of assessing the forecast is to use the timing-error—the difference in time between when the outcome crosses the threshold and when the forecast does so. When there is interest in the maximum value being reached, assessment of forecasts can be done using any of:

- the difference of times of the peaks;
- the difference in the peak values in the forecast and outcome;
- the difference between the peak value of the outcome and the value forecast for that time point.

- Forecast error can be a calendar forecast error or a cross-sectional forecast error, when we want to summarize the forecast error over a group of units. If we observe the average forecast error for a time-series of forecasts for the same product or phenomenon, then we call this a calendar forecast error or time-series forecast error. If we observe this for multiple products for the same period, then this is a cross-sectional performance error. Reference class forecasting has been developed to reduce forecast error. Combining forecasts has also been shown to reduce forecast error.
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- In statistics, a

- ↑ J. Scott Armstrong (2001). "Combining Forecasts". Kluwer Academic Publishers. http://marketing.wharton.upenn.edu/ideas/pdf/Armstrong/CombiningForecasts.pdf.
- ↑ J. Andreas Graefe, Scott Armstrong, Randall J. Jones, Jr. and Alfred G. Cuzán (2010). "Combining forecasts for predicting U.S. Presidential Election outcomes". https://dl.dropbox.com/u/3662406/Articles/Graefe_et_al_Combining.pdf.

### 2006

- (Hyndman & Koehler, 2006) ⇒ Rob J. Hyndman, and A. B. Koehler. (2006). “Another Look at Measures of Forecast Accuracy.” In: International Journal of Forecasting, 22(4). [doi>10.1016/j.ijforecast.2006.03.001
- QUOTE: Let [math]\displaystyle{ Y_t }[/math] denote the observation at time [math]\displaystyle{ t }[/math] and [math]\displaystyle{ F_t }[/math] denote the forecast of [math]\displaystyle{ Y_t }[/math]. Then define the forecast error [math]\displaystyle{ e_t = Y_t - F_t }[/math].