# MAAPE - Mean Arctangent Absolute Percentage Error

Calculates the mean arctangent percentage error (MAAPE) between the forecast and the eventual outcomes.

## Syntax

MAAPE(X, F)
X
is the eventual outcome time series sample data (a one-dimensional array of cells e.g. row or column).
F
is the forecast time series data (a one-dimensional array of cells (e.g. row or column).

## Remarks

1. The time series is homogeneous or equally spaced.
2. The time series X and F must be of identical size
3. The time series X or F may include observations with missing values (e.g. #N/A or blank).
4. Observations with missing values in Y or F are excluded from the MAAPE calculation.
5. The arctangent absolute percentage error (AAPE) for a given observation is defined as follows:

$${\displaystyle {\mathrm{AAPE_t}=\mathrm{arctan}(\left | \frac{y_t-f_t}{y_t}\right |)}}$$
Where:
• $\{y_t\}$ is the actual outcome value at period t.
• $\{f_t\}$ is the forecast value at period t.
6. Unlike the regular absolute percentage error (APE), the arctangent absolute error approaches to $\frac{\pi}{2}$ when division by zero occurs.
7. The AAPE is undefined when $y_t=f_t=0$, which can be found often in an intermittent demand time series.
8. The mean arctangent absolute percentage error (MAAPE) is defined as follows:

$${\displaystyle {\mathrm{MAAPE}= \frac{1}{N}\sum_{t=1}^N \mathrm{AAPE_t}=\frac{1}{N}\sum_{t=1}^N{\mathrm{arctan}(\left |\frac{y_t-f_t}{y_t} \right |)}}}$$
9. Although MAAPE is finite when response variable (i.e. $y_t$) equals zero, it has a nice trigonometric representation. However, because MAAPE’s value is expressed in radians, this makes MAAPE less intuitive.
10. Please note that MAAPE does not have a symmetric version, since division by zero is no longer a concern.
11. The MAAPE is also scale-free because its values are expressed in radians.
12. The MAAPE function is available starting with version 1.65 HAMMOCK.

## Examples

Example 1:

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A B C
Date Data Forecast
2008-01-01 -2.9 -2.95
2008-02-01 -2.83 -2.7
2008-03-01 -0.95 -1.00
2008-04-01 -0.88 -0.68
2008-05-01 1.21 1.50
2008-06-01 -1.67 -1.00
2008-07-01 0.83 0.90
2008-08-01 -0.27 -0.37
2008-09-01 1.36 1.26
2008-10-01 -0.34 -0.54
2008-11-01 0.48 0.58
2008-12-01 -2.83 -2.13
2009-01-01 -0.95 -0.75
2009-02-01 -0.88 -0.89
2009-03-01 1.21 1.25
2009-04-01 -1.67 -1.65
2009-05-01 -2.99 -3.20
2009-06-01 1.24 1.29
2009-07-01 0.64 0.60

Formula Description (Result)
=MAAPE($B$3:$B$21,$C$3:$C$21) MAAPE (0.151818)