Forecasting Multiplicative decomposition
12 seasons
Input Data Seasonal Index Computation
Forecast Error analysis
Period
Actual
value (Y)
Time
period (X)
Centered
average
Seasonal
ratio
Seasonal
index
Unseasona
lized value
Unseasona
lized
Forecast
Seasonaliz
ed Forecast
Error
Absolute
error
Squared error
Absolute
% error
Month 1 59042 1 1.306 45211.783 40731.268 53190.902 5851.098 5851.098 34235344.895 9.91%
Month 2 62659 2 1.505 41627.096 40847.757 61485.904 1173.096 1173.096 1376155.205 1.87%
Month 10 58435 10 41979.417 1.392 1.391 42011.750 41779.670 58112.194 322.806 322.806 104203.531 0.55%
Month 11 87705 11 42060.417 2.085 2.024 43324.859 41896.159 84812.800 2892.200 2892.200 8364820.839 3.30%
Month 12 77430 12 42066.958 1.841 1.819 42570.063 42012.648 76416.125 1013.875 1013.875 1027941.667 1.31%
Month 13 57495 13 42060.042 1.367 1.306 44027.158 42129.137 55016.376 2478.624 2478.624 6143575.566 4.31%
Month 14 62622 14 42240.292 1.483 1.505 41602.516 42245.626 63590.038 -968.038 968.038 937098.477 1.55%
Month 15 24273 15 42488.917 0.571 0.610 39786.999 42362.115 25844.010 -1571.010 1571.010 2468072.094 6.47%
Month 16 30492 16 42700.458 0.714 0.707 43105.849 42478.604 30048.303 443.697 443.697 196867.393 1.46%
Month 17 28237 17 42803.417 0.660 0.683 41321.515 42595.093 29107.298 -870.298 870.298 757418.096 3.08%
Month 18 17893 18 42861.375 0.417 0.449 39847.040 42711.582 19179.300 -1286.300 1286.300 1654567.723 7.19%
Month 19 21126 19 42876.750 0.493 0.471 44899.918 42828.071 20151.169 974.831 974.831 950296.333 4.61%
Month 20 22876 20 42997.750 0.532 0.512 44668.793 42944.560 21992.977 883.023 883.023 779729.536 3.86%
Month 21 22641 21 43302.292 0.523 0.520 43500.413 43061.049 22412.320 228.680 228.680 52294.358 1.01%
Month 22 60796 22 43494.000 1.398 1.391 43709.187 43177.538 60056.518 739.482 739.482 546834.057 1.22%
Month 23 87815 23 43596.500 2.014 2.024 43379.197 43294.027 87642.585 172.415 172.415 29726.951 0.20%
Month 24 78711 24 43745.417 1.799 1.819 43274.341 43410.516 78958.685 -247.685 247.685 61348.030 0.31%
Month 25 56583 25 43762.917 1.293 1.306 43328.789 43527.005 56841.850 -258.850 258.850 67003.479 0.46%
Month 26 66438 26 43713.250 1.520 1.505 44137.650 43643.494 65694.173 743.827 743.827 553278.078 1.12%
Month 27 27766 27 43825.250 0.634 0.610 45512.538 43759.983 26696.812 1069.188 1069.188 1143161.973 3.85%
Month 28 31600 28 43906.417 0.720 0.707 44672.203 43876.472 31037.120 562.880 562.880 316834.300 1.78%
Month 29 29589 29 43854.250 0.675 0.683 43300.007 43992.961 30062.529 -473.529 473.529 224229.742 1.60%
Month 30 20115 30 43863.542 0.459 0.449 44795.350 44109.450 19807.002 307.998 307.998 94862.919 1.53%
Month 31 19324 31 43881.042 0.440 0.471 41070.057 44225.939 20808.884 -1484.884 1484.884 2204880.152 7.68%
Month 32 23486 32 43872.750 0.535 0.512 45859.909 44342.428 22708.860 777.140 777.140 603946.374 3.31%
Month 33 24719 33 43904.208 0.563 0.520 47492.899 44458.917 23139.880 1579.120 1579.120 2493620.602 6.39%
Month 34 60666 34 43866.542 1.383 1.391 43615.724 44575.406 62000.841 -1334.841 1334.841 1781800.863 2.20%
Month 35 86693 35 43926.542 1.974 2.024 42824.947 44691.895 90472.370 -3779.370 3779.370 14283636.785 4.36%
Month 36 80056 36 44066.292 1.817 1.819 44013.806 44808.384 81501.245 -1445.245 1445.245 2088733.895 1.81%
Month 37 55658 37 44251.083 1.258 1.306 42620.464 44924.873 58667.324 -3009.324 3009.324 9056032.922 5.41%
Month 38 67164 38 44380.750 1.513 1.505 44619.964 45041.362 67798.308 -634.308 634.308 402346.945 0.94%
Month 39 27795 39 44444.917 0.625 0.610 45560.073 45157.851 27549.615 245.385 245.385 60213.776 0.88%
Month 40 30667 40 44553.292 0.688 0.707 43353.242 45274.340 32025.937 -1358.937 1358.937 1846708.930 4.43%
Month 41 31962 41 44661.917 0.716 0.683 46772.612 45390.829 31017.760 944.240 944.240 891588.509 2.95%
Month 42 21096 42 44781.917 0.471 0.449 46980.001 45507.318 20434.703 661.297 661.297 437313.067 3.13%
Month 43 22778 43 0.471 48410.979 45623.807 21466.599 1311.401 1311.401 1719772.037 5.76%
Month 44 23144 44 0.512 45192.103 45740.296 23424.743 -280.743 280.743 78816.755 1.21%
Month 45 26601 45 0.520 51108.807 45856.785 23867.439 2733.561 2733.561 7472354.652 10.28%
Month 46 61385 46 1.391 44132.648 45973.274 63945.165 -2560.165 2560.165 6554442.601 4.17%
Month 47 88581 47 2.024 43757.589 46089.763 93302.155 -4721.155 4721.155 22289303.012 5.33%
Slope 116.489
Seasonal Ratios
Season 1 Season 2 Season 3 Season 4 Season 5 Season 6 Season 7 Season 8 Season 9
Season 10
Season 11 Season 12
1.367 1.483 0.571 0.714 0.660 0.417 0.493 0.532 0.523 1.398 2.014 179.93%
1.293 1.520 0.634 0.720 0.675 0.459 0.440 0.535 0.563 1.383 1.974 181.67%
Forecasts for future periods
Period
Unseasona
lized
forecast
Seasonal
index
Seasonaliz
ed forecast
49.000 46322.741 1.306 60492.798
50.000 46439.230 1.505 69902.443
51.000 46555.719 0.610 28402.418
Problem 11-39
Month 3 22879 3 0.610 37502.029 40964.246 24991.207 -2112.207 2112.207 4461419.769 9.23%
Month 4 29946 4 0.707 42333.981 41080.735 29059.486 886.514 886.514 785907.894 2.96%
Month 5 26839 5 0.683 39275.707 41197.224 28152.066 -1313.066 1313.066 1724143.321 4.89%
Month 6 19134 6 0.449 42610.700 41313.713 18551.598 582.402 582.402 339191.773 3.04%
Month 7 20051 7 41908.042 0.478 0.471 42615.179 41430.202 19493.453 557.547 557.547 310858.391 2.78%
Month 8 19625 8 41842.042 0.469 0.512 38320.732 41546.691 21277.094 -1652.094 1652.094 2729414.455 8.42%
Month 9 19925 9 41898.583 0.476 0.520 38282.131 41663.181 21684.761 -1759.761 1759.761 3096758.797 8.83%
52.000 46672.208 0.707 33014.754
53.000 46788.697 0.683 31972.992
56.000 47138.164 0.512 24140.626
57.000 47254.653 0.520 24594.999
58.000 47371.142 1.391 65889.488
59.000 47487.631 2.024 96131.940
60.000 47604.121 1.819 86586.365
54.000 46905.186 0.449 21062.405
55.000 47021.675 0.471 22124.315
0
30000
40000
50000
90000
100000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
Value
Period
Actual vs. Forecast
Actual value (Y)
Seasonalized Forecast