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MAAPE
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:
Where:
 is the actual outcome value at period t.
 is the forecast value at period t.
 Unlike the regular absolute percentage error (APE), the arctangent absolute error approaches to when division by zero occurs.
 The AAPE is undefined when , which can be found often in an intermittent demand time series.
 The mean arctangent absolute percentage error (MAAPE) is defined as follows:
 Although MAAPE is finite when response variable (i.e. ) 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(3:21,3:21)  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