# MAE - Mean Absolute Error

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

1. The mean absolute error is a common measure of forecast error in time series analysis.
2. The time series is homogeneous or equally spaced.
3. The two time series must be identical in size.
4. 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

## Examples

Example 1:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A B C
Date Series1 Series2
1/1/2008 #N/A -2.61
1/2/2008 -2.83 -0.28
1/3/2008 -0.95 -0.90
1/4/2008 -0.88 -1.72
1/5/2008 1.21 1.92
1/6/2008 -1.67 -0.17
1/7/2008 0.83 -0.04
1/8/2008 -0.27 1.63
1/9/2008 1.36 -0.12
1/10/2008 -0.34 0.14
1/11/2008 0.48 -1.96
1/12/2008 -2.83 1.30
1/13/2008 -0.95 -2.51
1/14/2008 -0.88 -0.93
1/15/2008 1.21 0.39
1/16/2008 -1.67 -0.06
1/17/2008 -2.99 -1.29
1/18/2008 1.24 1.41
1/19/2008 0.64 2.37

Formula Description (Result)
=MAE($B$3:$B$21,$C$3:$C$21) MAE (1.366)