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A forecast is never completely accurate; forecasts will always deviate from the actualdemand. The objective of forecasting is that it be as slight as possible. There are manymeasures of forecast error, the more popular ones are; mean absolute deviation (MAD),mean absolute percent deviation (MAPD), cumulative error, and average error or bias(E).

MEAN ABSOLUTE DEVIATION (MAD) Most popular and simplest to use measure of forecasting MAD is and average of the difference between the forecast and the actual demand Formula: MAD= (Sum |Dt- Ft|)

nWhere: t = the period number

Dt= the demand in period tFt= the forecast for period tn = the total number of periods| | = the absolute value

The smaller/lower value of MAD, the more accurate the forecast One benefit of MAD is to compare the accuracy of several different forecastingtechiniques.

MEAN ABSOLUTE PERCENT DEVIATION (MAPD) Measures the absolute error as a percentage of demand rather than per period. Resulting in elimination of the problem fo interpreting the measure of accuracy relativeto the magnitude of the demand and forecast values, as MAD does. Formula: MAPD= (Sum |Dt- Ft|)

Sum(Dt)

CUMULATIVE ERROR Formula: E= Sum(et) A large postive value indicates the forecast is probably consistently lower than theactual demand, or is biased low. A large negative value implies the forecast is consistently higher than actual demandor is biased high. The cumulative error for exponential smoothing forecast is simply the sum of thevalues in the error column.

MAPE

Calculates the mean absolute percentage error (Deviation) function for the forecast and the eventual

outcomes.

Syntax

MAPEi(X,Y, Ret_type)

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Xis the original (eventual outcomes) time series sample data (a one dimensional array of cells (e.g.

rows or columns)).

Yis the forecast time series data (a one dimensional array of cells (e.g. rows or columns)).

Ret_typeis a switch to select the return output (1=MAPE (default), 2=Symmetric MAPE (SMAPI)).

Order Description

1 MAPE (default)

2 SMAPE

Remarks

1. MAPE is also referred to as MAPD.

2. The time series is homogeneous or equally spaced.

3. For a plain MAPE calculation, in the event that an observation value (i.e. ) is equal to zero, the

MAPE function skips that data point.

4. The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation

(MAPD), measures the accuracy of a method for constructing fitted time series values in statistics.

5. The two time series must be identical in size.

6. The mean absolute percentage error (MAPE) is defined as follows:

7. Where:

o is the actual observations time series

o is the estimated or forecasted time series

o is the number of non-missing data points

8. When calculating the average MAPE for a number of time series, you may encounter a problem: a

few of the series that have a very high MAPE might distort a comparison between the average

MAPE of a time series fitted with one method compared to the average MAPE when using another

method.

9. In order to avoid this problem, other measures have been defined, for example the SMAPE

(symmetrical MAPE), weighted absolute percentage error (WAPE), real aggregated percentage

error, and relative measure of accuracy (ROMA).

10.The symmetrical mean absolute percentage error (SMAPE) is defined as follows:

11.The SMAPE is easier to work with than MAPE, as it has a lower bound of 0% and an upper bound

of 200%.

12.The SMAPE does not treat over-forecast and under-forecast equally.

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13.For a SMAPE calculation, in the event the sum of the observation and forecast values

(i.e. ) equals zero, the MAPE function skips that data point.

14.Mean Absolute Percent Error (MAPE) is the most common measure of forecast error. MAPEfunctions best when there are no extremes to the data (including zeros).

15.With zeros or near-zeros, MAPE can give a distorted picture of error. The error on a near-zero

item can be infinitely high, causing a distortion to the overall error rate when it is averaged in.

For forecasts of items that are near or at zero volume,Symmetric Mean Absolute Percent Error

(SMAPE)is a better measure.

16.MAPE is the average absolute percent error for each time period or forecast minus actuals

divided by actuals:

17.

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