Calculates the mean absolute error function for the forecast and the eventual outcomes.

## Syntax

**MAE**(**X**, **Y**)

- X
- is the original (eventual outcomes) time series sample data (a one-dimensional array of cells (e.g., rows or columns)).
- Y
- is the forecast time series data (a one-dimensional array of cells (e.g., rows or columns)).

## Remarks

- The mean absolute error is a common measure of forecast error in time series analysis.
- The time series is homogeneous or equally spaced.
- The two time series must be identical in size.
- The mean absolute error is given by: $$\mathrm{MAE}=\frac{\mathrm{SAE}}{N}=\frac{\sum_{i=1}^N \left | x_i - \hat x_i \right |}{N}$$ Where:
- $\{x_i\}$ is the actual observations time series.
- $\{\hat x_i\}$ is the estimated or forecasted time series.
- $\mathrm{SAE}$ is the sum of the absolute errors (or deviations).
- $N$ is the number of non-missing data points.

## Files Examples

## Related Links

## References

- Hamilton, J.D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6.
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.

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