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

- 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: $$ {\displaystyle {\mathrm{AAPE_t}=\mathrm{arctan}(\left | \frac{y_t-f_t}{y_t}\right |)}} $$ Where:
- $\{y_t\}$ is the actual outcome value at period $t$.
- $\{f_t\}$ is the forecast value at period $t$.

- 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: $${\displaystyle {\mathrm{MAAPE}= \frac{1}{N}\sum_{t=1}^N \mathrm{AAPE_t}=\frac{1}{N}\sum_{t=1}^N{\mathrm{arctan}(\left |\frac{y_t-f_t}{y_t} \right |)}}}$$
- Although MAAPE is finite when the 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 has no symmetric version since division by zero is no longer a concern.
- The MAAPE is also scale-free because its values are expressed in radians.
- The MAAPE function is available starting with version 1.65 HAMMOCK.

## 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. 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.

## Comments

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