A forecast is never completely accurate; forecasts will always deviate from the actual demand. The objective of forecasting is that it be as slight as possible. There are many measures 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|)
                                n
Where: t = the period number
           Dt = the demand in period t
           Ft = the forecast for period t
           n = 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 forecasting techiniques.

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 relative to 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 the actual demand, or is biased low.
A large negative value implies the forecast is consistently higher than actual demand or is biased high.
The cumulative error for exponential smoothing forecast is simply the sum of the values in the error column.

AVERAGE ERROR
A measure closely related to cumulative error is the average error or bias. It is computed by averaging the cumulative error over the number of time periods.
Formula: E= Sum (et)
                          n
A positive value indicates low bias and a negative value indicates a high bias. A value close to zero implies a lack of bias.

FORECAST CONTROL
There are several ways to monitor forecast error over time to make sure the forecast is performed correctly.

Can provide inaccurate forecasts for several reasons;
      Change in trend
      Unanticipated appearance of a cycle
      Irregular variation
      Promotional campaign
      New competition
      Politcial event that distracts consumers
           A tracking signal monitors the forecast to see if it is high or low. It is recomputed each period and each movement is compared to control limits.
           It is computed as simply the error divided by MAD.

Forecast errors are typically normally distributed which results in the following relationship between MAD and the standard deviation of the distribution of error: 1MAD is about 0.8 stadard deviations. This enables us to establish statistical control limits for the tracking signal that corresponds to the more familiar normal distribution.
      Statistical control charts are another method for monitoring forecast error.
      For example, 3 stadard deviation, control limits would reflect 99.7 percent of the forecast errors (assuming they are normally distributed).
      Formula: Divide the Sum (Dt - Ft)^2
                               n-1
      This formula without the square root is the mean squared error (MSE).
           MSE is the average of the squared forecast errors and is sometimes used as a measure of forecast error.