# Forecasting

Forecasting is the process of estimation in unknown situations. Prediction is a similar, but more general term, and usually refers to estimation of time series, cross-sectional or longitudinal data. In more recent years, Forecasting has evolved into the practice of 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 consensus process.

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

## Categories of forecasting methods

### Time series methods

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

### 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.

e.g. Box-Jenkins

### Judgemental methods

Judgemental forecasting methods incorporate intuitive judgements, opinions and probability estimates.

## Forecasting accuracy

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

${\displaystyle \ E_{t}=Y_{t}-F_{t}}$

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:

 Mean Absolute Error (MAE) ${\displaystyle \ MAE={\frac {\sum _{t=1}^{N}|E_{t}|}{N}}}$ Mean Absolute Percentage Error (MAPE) ${\displaystyle \ MAPE={\frac {\sum _{t=1}^{N}|{\frac {E_{t}}{Y_{t}}}|}{N}}}$ Percent Mean Absolute Deviation (PMAD) ${\displaystyle \ PMAD={\frac {\sum _{t=1}^{N}|E_{t}|}{\sum _{t=1}^{N}|Y_{t}|}}}$ Mean squared error (MSE) ${\displaystyle \ MSE={\frac {\sum _{t=1}^{N}{E_{t}^{2}}}{N}}}$ Root Mean squared error (RMSE) ${\displaystyle \ RMSE={\sqrt {\frac {\sum _{t=1}^{N}{E_{t}^{2}}}{N}}}}$

Please note that the business forecasters and demand planners in the industry refer to the PMAD as the MAPE, although they compute this volume weighted MAPE. Difference between MAPE and WMAPE is explained in Calculating Demand Forecast Accuracy