In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, a forecast error is the difference between the actual or real and the predicted or forecast

Forecasting

Forecasting is the process of making statements about events whose actual outcomes have not yet been observed. A commonplace example might be estimation for some variable of interest at some specified future date. Prediction is a similar, but more general term...

 value of a time series

Time series

In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...

 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

Reference class forecasting

Reference class forecasting is the method of predicting the future, through looking at similar past situations and their outcomes.Reference class forcasting predicts the outcome of a planned action based on actual outcomes in a reference class of similar actions to that being forecast. The theories...

 has been developed to reduce forecast error.

See also

• Forecasting
  Forecasting
  Forecasting is the process of making statements about events whose actual outcomes have not yet been observed. A commonplace example might be estimation for some variable of interest at some specified future date. Prediction is a similar, but more general term...
  
  
• Calculating Demand Forecast Accuracy
  Calculating Demand Forecast Accuracy
  Calculating demand forecast accuracy is the process of determining the accuracy of forecasts made regarding customer demand for a product.-Importance of forecasts:...
  
  
• Mean squared prediction error
• Errors and residuals in statistics
  Errors and residuals in statistics
  In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
  
  
• Optimism bias
  Optimism bias
  Optimism bias is the demonstrated systematic tendency for people to be overly optimistic about the outcome of planned actions. This includes over-estimating the likelihood of positive events and under-estimating the likelihood of negative events. Along with the illusion of control and illusory...
  
  
• Reference class forecasting
  Reference class forecasting
  Reference class forecasting is the method of predicting the future, through looking at similar past situations and their outcomes.Reference class forcasting predicts the outcome of a planned action based on actual outcomes in a reference class of similar actions to that being forecast. The theories...