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 onedimensional array of cells e.g. row or column).
 F
 is the forecast time series data (a onedimensional array of cells (e.g. row or column).
Remarks
 The time series is homogeneous or equally spaced.
 The time series X and F must be of identical size
 The time series X or F may include observations with missing values (e.g. #N/A or blank).
 Observations with missing values in Y or F are excluded from the MAAPE calculation.
 The arctangent absolute percentage error (AAPE) for a given observation is defined as follows:
$$ {\displaystyle {\mathrm{AAPE_t}=\mathrm{arctan}(\left  \frac{y_tf_t}{y_t}\right )}} $$
Where:
 $\{y_t\}$ is the actual outcome value at period t.
 $\{f_t\}$ is the forecast value at period t.
 Unlike the regular absolute percentage error (APE), the arctangent absolute error approaches to $\frac{\pi}{2}$ when division by zero occurs.
 The AAPE is undefined when $y_t=f_t=0$, which can be found often in an intermittent demand time series.
 The mean arctangent absolute percentage error (MAAPE) is defined as follows:
$${\displaystyle {\mathrm{MAAPE}= \frac{1}{N}\sum_{t=1}^N \mathrm{AAPE_t}=\frac{1}{N}\sum_{t=1}^N{\mathrm{arctan}(\left \frac{y_tf_t}{y_t} \right )}}}$$  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.
 Please note that MAAPE does not have a symmetric version, since division by zero is no longer a concern.
 The MAAPE is also scalefree because its values are expressed in radians.
 The MAAPE function is available starting with version 1.65 HAMMOCK.
Examples
Example 1:


Formula  Description (Result) 

=MAAPE($B$3:$B$21,$C$3:$C$21)  MAAPE (0.151818) 
Files Examples
References
 R.J. Hyndman, A.B. Koehler, "Another look at measures of forecast accuracy", International Journal of Forecasting, 22 (2006), pp. 679688
 James Douglas Hamilton; Time Series Analysis; Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896
 Tsay, Ruey S.; Analysis of Financial Time Series; John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0471690740
 D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
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