Forecast errors and seasonal correlation

After LN calculates the demand forecast for a plan item, LN determines the forecast errors and any seasonal correlation.

LN calculates the following fields in the Plan Items - Forecast Settings (cpdsp1110m000) session:

  • Average Forecast Error (AFCE)
  • Mean Absolute Deviation (MAD)
  • Mean Relative Deviation (MRD)
  • Standard Deviation (SDEV)
  • Seasonal Correlation Factor (COR)

The calculations are based on the following formulas:

Average forecast error
AFCE = sum(FD(t) - AD(t)) / n
AFCEthe Average Forecast Error field
sum()the sum of all historical periods
FD(t)the forecast demand for period t
AD(t)the actual demand for period t
nthe number of historical periods

 

Mean absolute forecast error
MAD = sum(abs(FD(t) -	 AD(t))) / n
MADthe Mean Absolute Deviation field
sum()the sum of all historical periods
abs(FD(t)-AD(t))the absolute value of (FD(t)-AD(t))
FD(t)the forecast demand for period t
AD(t)the actual demand for period t
nthe number of historical periods

 

Mean relative forecast error
MRD = sum(100 * abs((FD(t) - AD(t))) / AD(t)) / n
MRDMean Relative Deviation
sumthe sum of all historical periods
FD(t)the forecast demand for period t
AD(t)he actual demand for period t
nthe number of historical periods

 

Standard deviation of the forecast error
SDEV = sqr(sum(((FD(t) - AD(t)) - AFCE)^2) / (n - 1))
SDEVthe Standard Deviation field
sqr()the square root
sum()the sum of all historical periods
FD(t)the forecast demand for period t
AD(t)the actual demand for period t
AFCEthe mean forecast error
nthe number of historical periods

 

Seasonal correlation

LN determines the standard deviation from the actual demand for two sets of data. Data set one consists of the periods from the first period to the last period minus the season length in periods. Data set two consists of the periods from the first period after the season length in periods up to the last period. In other words, data set two is shifted by a season length compared to data set one.

The following diagram illustrates this for a season length of one month.

[...]
AData set 1
BData set 2
1January
2February
3March
4April
5May
Standard deviations:
SDV1 = sqr(sum(((DM(t) - DM1)^2) / (m - 1)) SDV2 =
			 sqr(sum(((DM(t+L) - DM2)^2) / (m - 1))
SDV1the standard deviation for data set one
SDV2the standard deviation for data set two
sqr()the square root
sum()the sum for all historical periods
DM(t)the trend-adjusted actual demand for period t (*)
DM1the trend-adjusted average demand for data set one (*)
DM2the trend-adjusted average demand for data set two (*)
Lthe season length in periods
mthe number of historical periods minus the season length in periods

 

(*) For the calculation of the trend-adjusted average demand, see Forecast method: polynomial regression.

LN determines the covariance factor for the two sets of data.

COV = sum((DM(t) - DM1) x (DM(t+L) - DM2) / (m - 1))
COVcovariance factor
sumthe sum of all periods minus the season length in periods
DM(t)the trend-adjusted actual demand for period t
DM1the trend-adjusted average demand for data set one
DM2the trend-adjusted average demand for data set two
Lthe season length in periods
mthe number of historical periods minus the season length in periods

 

Finally, the seasonal correlation factor is computed as follows:

COR = COV / (SDV1 x SDV2)
CORthe Seasonal Correlation Factor field
COVcovariance factor
SDV1standard deviation for data set one
SDV2standard deviation for data set two