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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. Since the forecast error is derived from the same scale of data, comparisons between the forecast errors of different series can only be made when the series are on the same scale.[1]
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.[2][3]
^J. Scott Armstrong (2001). "Combining Forecasts". Principles of Forecasting: A Handbook for Researchers and Practitioners(PDF). Kluwer Academic Publishers.
^J. Andreas Graefe; Scott Armstrong; Randall J. Jones, Jr.; Alfred G. Cuzán (2010). "Combining forecasts for predicting U.S. Presidential Election outcomes" (PDF).
In statistics, a forecasterror is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon...
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the error involved in measuring the initial conditions, and an incomplete understanding of atmospheric and related processes. Hence, forecasts become...
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achieved, for example, by forecasting the spread and exiting at forecasterror bounds. A common way to model, and forecast, the spread for risk management...
mean absolute percentage error (MAPE) for a utility with 1GW peak load is: $500,000 per year from long-term load forecasting, $300,000 per year from short-term...
error Mean absolute percentage error Mean squared error Root mean squared error Armstrong, J. S. (1985) Long-range Forecasting: From Crystal Ball to Computer...
track error by 15–20 percent. Using a consensus of forecast models, as well as ensemble members of the various models, can help reduce forecasterror. However...
disturbance several hundred miles south of the Gulf of Tehuantepec. Initially forecast to stay offshore and to only be a weak tropical storm at peak intensity...
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the sales forecast and the actual demand (i.e. the forecasterror). Typically, the higher the P:D ratio, the more the firm relies on forecasts and inventories...
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conditions required for running weather forecast models, a procedure known as data assimilation. The 'forecasterror covariance matrix' is typically constructed...
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frontogenesis. Forecasterrors need to be taken into account and can be determined either via absolute error, or by considering persistence and absolute error combined...
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