Forecasting is the process of estimation in unknown situations. Prediction is a similar, but more general term. Both can refer to estimation of time series, cross-sectional or longitudinal data. Usage can differ between areas of application: for example in hydrology, the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific future times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. Risk and uncertainty are central to forecasting and prediction. Forecasting is used in the practice of Customer Demand Planning in every day business forecasting for manufacturing companies. The discipline of demand planning, also sometimes referred to as supply chain forecasting, embraces both statistical forecasting and a consensus process.

Forecasting is commonly used in discussion of time-series data.

Time series methods

Time series methods use historical data as the basis of estimating future outcomes.

• Rolling forecast is a projection into the future based on past performances, routinely updated on a regular schedule to incorporate data.
• Moving average
• Exponential smoothing
• Extrapolation
• Linear prediction
• Trend estimation
• Growth curve
• Topics

Causal / econometric methods

Some forecasting methods use the assumption that it is possible to identify the underlying factors that might influence the variable that is being forecast. For example, sales of umbrellas might be associated with weather conditions. If the causes are understood, projections of the influencing variables can be made and used in the forecast.

• Regression analysis using linear regression or non-linear regression
• Autoregressive moving average (ARMA)
• Autoregressive integrated moving average (ARIMA)

e.g. Box-Jenkins

• Econometrics

Judgmental methods

Judgmental forecasting methods incorporate intuitive judgements, opinions and subjective probability estimates.

• Composite forecasts
• Surveys
• Delphi method
• Scenario building
• Technology forecasting
• Forecast by analogy

Other methods

• Simulation
• Prediction market
• Probabilistic forecasting and Ensemble forecasting
• Reference class forecasting

Forecasting accuracy

The forecast error is the difference between the actual value and the forecast value for the corresponding period.

$\backslash \; E\_t\; =\; Y\_t\; -\; F\_t$

where E is the forecast error at period t, Y is the actual value at period t, and F is the forecast for period t.

Measures of aggregate error:

^{N} |E_t|}{N} |- |Mean Absolute Percentage Error (MAPE) |$\backslash \; MAPE\; =\; \backslash frac\{\backslash sum\_\{t=1\}^N\; |\backslash frac\{E\_t\}\{Y\_t\}|\}\{N\}$ |- |Percent Mean Absolute Deviation (PMAD) |$\backslash \; PMAD\; =\; \backslash frac\{\backslash sum\_\{t=1\}^\{N\}\; |E\_t|\}\{\backslash sum\_\{t=1\}^\{N\}\; |Y\_t|\}$ |- |Mean squared error (MSE) |$\backslash \; MSE\; =\; \backslash frac\{\backslash sum\_\{t=1\}^N\; \{E\_t^2\}\}\{N\}$ |- |Root Mean squared error (RMSE) |$\backslash \; RMSE\; =\; \backslash sqrt\{\backslash frac\{\backslash sum\_\{t=1\}^N\; \{E\_t^2\}\}\{N\}\}$ |- |Forecast skill (SS) |$\backslash \; SS\; =\; 1-\; \backslash frac\{MSE\_\{forecast\}\}\{MSE\_\{ref\}\}$ |}