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:

 
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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)

Files Examples

References

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