Forecasting Multiplicative decomposition
4 seasons
Input Data Seasonal Index Computation Forecast Error analysis
Period
Actual
value (Y)
Time
period (X)
Centered
average
Seasonal
ratio
Seasonal
index
Unseason
alized
value
Unseason
alized
Forecast
Seasonali
zed
Forecast
Error
Absolute
error
Squared
error
Absolute
% error
Quarter 1 263 1 0.918 286.491 304.928 279.925 -16.925 16.925 286.471 6.44%
Quarter 2 300 2 0.940 318.981 308.002 289.674 10.326 10.326 106.618 3.44%
Seasonal Ratios
Season 1 Season 2 Season 3 Season 4
0.808 1.220
0.855 0.940 1.055 1.142
0.930 0.902
Average 0.918 0.940 0.924 1.190
Forecasts for future periods
Period
index
forecast
325.078
Unseaso
nalized
Seasonal
Seasonali
zed
18.000 357.188 0.940
335.933
333.058
20.000 363.336 1.190
432.261
Problem 11-46 (a)
Forecasting Additive decomposition
4 seasons
Input Data Seasonal Index Computation Forecast Error analysis
Period
Actual
value (Y)
Time
period (X)
Centered
average
Seasonal
ratio
Seasonal
index
Unseason
alized
value
Unseason
alized
Forecast
Seasonali
zed
Forecast
Error
Absolute
error
Squared
error
Absolute
% error
Quarter 1 263 1 -27.333 290.333 306.875 279.542 -16.542 16.542 273.627 6.29%
Quarter 2 300 2 -20.042 320.042 309.633 289.592 10.408 10.408 108.333 3.47%
Quarter 3 245 3 303.375 -58.375 -22.833 267.833 312.392 289.558 -44.558 44.558 1985.445 18.19%
Seasonal Ratios
Season 1 Season 2 Season 3 Season 4
-9.875 -6.625 -29.125 66.875
-24.000 -33.000
Average -27.333 -20.042 -22.833 61.708
Forecasts for future periods
Period
Unseaso
nalized
forecast
Seasonal
index
Seasonali
zed
forecast
17.000 351.008 -27.333
323.675
19.000 356.525 -22.833
333.692
420.992
Problem 11-46 (b)