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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 42.9 1 0.800 53.597 53.180 42.566 0.334 0.334 0.112 0.78%
Quarter 2 48.5 2 0.890 54.519 54.043 48.077 0.423 0.423 0.179 0.87%
Quarter 3 54.1 3 55.013 0.983 0.977 55.379 54.907 53.638 0.462 0.462 0.213 0.85%
Quarter 4 74.1 4 55.350 1.339 1.336 55.472 55.770 74.498 -0.398 0.398 0.159 0.54%
Seasonal Ratios
Season 1 Season 2 Season 3 Season 4
0.782 0.879 0.987 1.336
0.811 0.888 0.961 1.332
0.808 0.901
Average 0.800 0.890 0.977 1.336
Forecasts for future periods
Period
Unseason
alized
forecast
Seasonal
index
Seasonali
zed
forecast
17.000 66.996 0.800 53.624
18.000 67.859 0.890 60.368
19.000 68.723 0.977 67.135
20.000 69.586 1.336 92.954
Problem 11-40
Quarter 5 43.8 5 56.038 0.782 0.800 54.722 56.634 45.330 -1.530 1.530 2.342 3.49%
Quarter 6 50.3 6 57.213 0.879 0.890 56.542 57.497 51.150 -0.850 0.850 0.722 1.69%
Quarter 7 57.8 7 58.575 0.987 0.977 59.167 58.361 57.013 0.787 0.787 0.620 1.36%
Quarter 8 79.8 8 59.713 1.336 1.336 59.739 59.224 79.112 0.688 0.688 0.473 0.86%
Quarter 9 49.0 9 60.388 0.811 0.800 61.218 60.088 48.095 0.905 0.905 0.819 1.85%
Quarter 10 54.2 10 61.013 0.888 0.890 60.926 60.951 54.222 -0.022 0.022 0.000 0.04%
Quarter 12 83.3 12 62.525 1.332 1.336 62.359 62.678 83.726 -0.426 0.426 0.182 0.51%
Quarter 13 51.3 13 63.475 0.808 0.800 64.092 63.542 50.860 0.440 0.440 0.194 0.86%
Quarter 14 58.2 14 64.575 0.901 0.890 65.423 64.405 57.295 0.905 0.905 0.819 1.55%
Quarter 15 62.9 15 0.977 64.387 65.269 63.761 -0.861 0.861 0.742 1.37%
40.0
50.0
60.0
75.0
90.0
Actual vs. Forecast
