# SAE - Sum of Absolute Errors

Calculates the sum of absolute errors (SAE) between the forecast and the eventual outcomes.

## Syntax

SAE(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 time series is homogeneous or equally spaced.
2. The two time series must be identical in size.
3. A missing value (say $x_k$ or $\hat x_k$) in either time series will exclude the data point $(x_k,\hat x_k)$ from the SSE.
4. The sum of absolute errors (SAE) or deviations (SAD), is defined as follows:

$$\mathrm{SAE}=\mathrm{SAD}=\sum_{i=1}^N \left | x_i-\hat x_i \right |$$

Where:
• $\{x_i\}$ is the actual observations time series
• $\{\hat x_i\}$ is the estimated or forecasted time series

## 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)
=SAE($B$1:$B$19,$C$1:$C$19) SAE (24.59)