MRAE – Mean Relative Absolute Error

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 MRAE calculation.
5. 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.
6. NumXL uses the naïve forecasting model as a benchmark. The forecast value of the benchmark is defined as follows:
   
   $$ {\displaystyle f_t^*=\left\{\begin{matrix} y_{t-1} \\ y_{t-M} \end{matrix}\right. \begin{matrix} \mathrm{Non-Seasonal}\\ \mathrm{Seasonal} \end{matrix}} $$
7. The mean relative absolute error is given by the following formula:
   $$ \mathrm{MRAE}=\frac{1}{N}\sum_{i=1}^N\left |\frac{y_t-f_t}{y_t - f_t^*} \right | $$
8. The MRAE (mean relative absolute error) is sensitive to extreme values (i.e. outliers), and to low values.
9. 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!
10. The MRAE function is available starting with version 1.65 HAMMOCK.

Example 1:

Files Examples

Related Links

• Wikipedia - Approximation error

References

• R.J. Hyndman, A.B. Koehler, "Another look at measures of forecast accuracy", International Journal of Forecasting, 22 (2006), pp. 679-688
• 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: 0-471-690740
• D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906