# Mathematics Chapter 11 Homework Problem 11-48 Forecasting Seasons Seasonal Index Computation

Type Homework Help
Pages 2
Words 212
Authors Barry Render, Jr. Ralph M. Stair, Nagraj Balakrishnan

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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 1 294 1 0.806 364.846 381.687 307.571 -13.571 13.571 184.163 4.62%
Quarter 2 499 2 1.159 430.492 389.786 451.816 47.184 47.184 2226.342 9.46%
Quarter 3 437 3 398.625 1.096 1.139 383.630 397.886 453.239 -16.239 16.239 263.711 3.72%
Quarter 4 344 4 404.750 0.850 0.860 400.076 405.985 349.081 -5.081 5.081 25.818 1.48%
Seasonal Ratios
Season 1 Season 2 Season 3 Season 4
1.096 0.850
Forecasts for future periods
Period
Unseason
alized
forecast
Seasonal
index
Seasonali
zed
forecast
18.000 519.379 1.159
602.032
20.000 535.578 0.860
460.510
Problem 11-48 (a)
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 1 294 1 -85.000 379.000 387.032 302.032 -8.032 8.032 64.511 2.73%
Quarter 2 499 2 70.333 428.667 394.351 464.685 34.315 34.315 1177.550 6.88%
Quarter 3 437 3 398.625 38.375 59.417 377.583 401.671 461.087 -24.087 24.087 580.196 5.51%
Quarter 4 344 4 404.750 -60.750 -59.708 403.708 408.990 349.282 -5.282 5.282 27.895 1.54%
Slope 7.319
Seasonal Ratios
Season 1 Season 2 Season 3 Season 4
-82.250 85.625 102.750 -154.625
-168.500 67.750
Forecasts for future periods
Period
Unseason
alized
forecast
Seasonal
index
Seasonali
zed
forecast
17.000 504.142 -85.000
419.142
19.000 518.780 59.417
578.197
Problem 11-48 (b)

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