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 9027 1 1.001 9014.982 9051.176 9063.242 -36.242 36.242 1313.488 0.40%
Quarter 2 9092 2 1.001 9085.075 9163.686 9170.671 -78.671 78.671 6189.106 0.87%
Quarter 3 9194 3 9229.750 0.996 0.998 9216.624 9276.197 9253.426 -59.426 59.426 3531.507 0.65%
Quarter 4 9367 4 9351.500 1.002 1.002 9348.932 9388.708 9406.853 -39.853 39.853 1588.238 0.43%
Seasonal Ratios
Season 1 Season 2 Season 3 Season 4
1.003 0.997 0.997 1.003
1.000 1.005 1.000 1.001
1.001 1.000
Average 1.001 1.001 0.998 1.002
Forecasts for future periods
Period
Unseason
alized
forecast
Seasonal
index
Seasonaliz
ed
forecast
Problem 11-42
Quarter 5 9505 5 9480.000 1.003 1.001 9492.346 9501.218 9513.885 -8.885 8.885 78.939 0.09%
Quarter 6 9588 6 9617.875 0.997 1.001 9580.698 9613.729 9621.057 -33.057 33.057 1092.740 0.34%
Quarter 7 9726 7 9759.000 0.997 0.998 9749.934 9726.240 9702.364 23.636 23.636 558.638 0.24%
Quarter 8 9938 8 9910.000 1.003 1.002 9918.831 9838.751 9857.765 80.235 80.235 6437.624 0.81%
Quarter 9 10063 9 10061.125 1.000 1.001 10049.603 9951.261 9964.527 98.473 98.473 9696.844 0.98%
Quarter 10 10238 10 10185.625 1.005 1.001 10230.203 10063.772 10071.442 166.558 166.558 27741.450 1.63%
Quarter 11 10285 11 10286.125 1.000 0.998 10310.309 10176.283 10151.302 133.698 133.698 17875.032 1.30%
Quarter 12 10375 12 10361.375 1.001 1.002 10354.988 10288.793 10308.678 66.322 66.322 4398.649 0.64%
Quarter 13 10430 13 10417.750 1.001 1.001 10416.114 10401.304 10415.170 14.830 14.830 219.925 0.14%
Quarter 14 10473 14 10470.375 1.000 1.001 10465.024 10513.815 10521.828 -48.828 48.828 2384.183 0.47%
Quarter 15 10501 15 0.998 10526.841 10626.325 10600.240 -99.240 99.240 9848.667 0.95%