Calculates the mean relative absolute error (MRAE) between the forecast and the eventual outcomes.
Syntax
MRAE(X, F, M)
 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).
 M
 is the seasonal period in X. For nonseasonal time series, set M=1 (default), or leave it blank.
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 MRAE calculation.
 The relative absolute error for a given observation is defined as follows:
$$r_t=\left  \frac{y_t  f_t }{ y_t  f_t^*} \right $$
Where:
 $\{y_t\}$ is the actual outcome value at time t.
 $\{f_t\}$ is the forecast value at time t.
 $\{f_i^*\}$ is the forecast value of the benchmark model at time t.
 NumXL uses the naïve forecasting model as a benchmark. The forecast value of the benchmark is defined as follows:
$$ {\displaystyle f_t^*=\left\{\begin{matrix} y_{t1} \\ y_{tM} \end{matrix}\right. \begin{matrix} \mathrm{NonSeasonal}\\ \mathrm{Seasonal} \end{matrix}} $$  The mean relative absolute error is given by the following formula:
$$ \mathrm{MRAE}=\frac{1}{N}\sum_{i=1}^N\left \frac{y_tf_t}{y_t  f_t^*} \right  $$  The MRAE (mean relative absolute error) is sensitive to extreme values (i.e. outliers), and to low values.
 Division by zero may occur if the predictive value obtained by the reference (benchmark) model is equal to the actual value. In this case, the MRAE function returns #VALUE!
 The MRAE function is available starting with version 1.65 HAMMOCK.
Examples
Example 1:


Formula  Description (Result) 

=MRAE($B$3:$B$21,$C$3:$C$21,1)  MRAE (0.348) 
Files Examples
Related Links
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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