| Forecast errors and seasonal correlationAfter 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 |
(*) 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)) 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 |
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