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
AFCE | the 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 |
n | the number of historical periods |
Mean absolute forecast error
MAD = sum(abs(FD(t) - AD(t))) / n
MAD | the 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 |
n | the number of historical periods |
Mean relative forecast error
MRD = sum(100 * abs((FD(t) - AD(t))) / AD(t)) / n
MRD | Mean Relative Deviation |
sum | the sum of all historical periods |
FD(t) | the forecast demand for period t |
AD(t) | he actual demand for period t |
n | the number of historical periods |
Standard deviation of the forecast error
SDEV = sqr(sum(((FD(t) - AD(t)) - AFCE)^2) / (n - 1))
SDEV | the 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 |
AFCE | the mean forecast error |
n | the 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.
Standard deviations:
SDV1 = sqr(sum(((DM(t) - DM1)^2) / (m - 1)) SDV2 =
sqr(sum(((DM(t+L) - DM2)^2) / (m - 1))
SDV1 | the standard deviation for data set one |
SDV2 | the 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 (*) |
DM1 | the trend-adjusted average demand for data set one (*) |
DM2 | the trend-adjusted average demand for data set two (*) |
L | the season length in periods |
m | the number of historical periods minus the season length in
periods |
LN determines the covariance factor for the two
sets of data.
(*) For the calculation
of the trend-adjusted average demand, see Forecast method: polynomial regression.
COV = sum((DM(t) - DM1) x (DM(t+L) - DM2) / (m - 1))
COV | covariance factor |
sum | the sum of all periods minus the season length in periods |
DM(t) | the trend-adjusted actual demand for period t |
DM1 | the trend-adjusted average demand for data set one |
DM2 | the trend-adjusted average demand for data set two |
L | the season length in periods |
m | the number of historical periods minus the season length in
periods |
Finally, the seasonal
correlation factor is computed as follows:
COR = COV / (SDV1 x SDV2)
COR | the Seasonal Correlation Factor field |
COV | covariance factor |
SDV1 | standard deviation for data set one |
SDV2 | standard deviation for data set two |