Forecasting Multiplicative decomposition
12 seasons
Input Data Seasonal Index Computation Forecast Error analysis
Unseason
Unseason
Seasonali
Month 9 3.280 9 3.245 1.011 1.013 3.239 3.246 3.288 -0.008 0.008 0.000 0.24%
Month 10 3.274 10 3.284 0.997 1.003 3.265 3.258 3.267 0.007 0.007 0.000 0.21%
Month 11 3.264 11 3.314 0.985 0.995 3.282 3.270 3.252 0.012 0.012 0.000 0.36%
Month 12 3.298 12 3.346 0.986 0.984 3.352 3.282 3.229 0.069 0.069 0.005 2.09%
Month 13 3.301 13 3.383 0.976 0.977 3.378 3.293 3.219 0.082 0.082 0.007 2.50%
Month 14 3.369 14 3.410 0.988 0.986 3.416 3.305 3.259 0.110 0.110 0.012 3.25%
Month 15 3.541 15 3.434 1.031 1.003 3.529 3.317 3.328 0.213 0.213 0.045 6.01%
Month 16 3.506 16 3.458 1.014 1.013 3.462 3.329 3.371 0.135 0.135 0.018 3.85%
Month 17 3.498 17 3.482 1.005 1.035 3.381 3.341 3.456 0.042 0.042 0.002 1.20%
Month 18 3.617 18 3.502 1.033 1.040 3.478 3.352 3.487 0.130 0.130 0.017 3.61%
Month 19 3.593 19 3.517 1.022 1.013 3.546 3.364 3.409 0.184 0.184 0.034 5.13%
Month 20 3.510 20 3.529 0.995 1.005 3.492 3.376 3.393 0.117 0.117 0.014 3.32%
Month 21 3.582 21 3.530 1.015 1.013 3.537 3.388 3.431 0.151 0.151 0.023 4.21%
Month 22 3.559 22 3.528 1.009 1.003 3.549 3.400 3.409 0.150 0.150 0.022 4.21%
Month 23 3.555 23 3.540 1.004 0.995 3.574 3.411 3.393 0.162 0.162 0.026 4.56%
Month 24 3.489 24 3.551 0.983 0.984 3.546 3.423 3.368 0.121 0.121 0.015 3.45%
Month 25 3.472 25 3.547 0.979 0.977 3.553 3.435 3.357 0.115 0.115 0.013 3.31%
Month 26 3.484 26 3.539 0.984 0.986 3.533 3.447 3.399 0.085 0.085 0.007 2.44%
Month 27 3.447 27 3.534 0.975 1.003 3.435 3.459 3.470 -0.023 0.023 0.001 0.67%
Month 28 3.564 28 3.523 1.012 1.013 3.519 3.470 3.514 0.050 0.050 0.002 1.39%
Month 29 3.729 29 3.503 1.065 1.035 3.604 3.482 3.602 0.127 0.127 0.016 3.39%
Month 30 3.640 30 3.476 1.047 1.040 3.500 3.494 3.634 0.006 0.006 0.000 0.17%
Month 31 3.482 31 1.013 3.437 3.506 3.552 -0.070 0.070 0.005 2.01%
Month 32 3.427 32 1.005 3.409 3.517 3.536 -0.109 0.109 0.012 3.17%
Month 33 3.531 33 1.013 3.486 3.529 3.574 -0.043 0.043 0.002 1.23%
Month 34 3.362 34 1.003 3.353 3.541 3.551 -0.189 0.189 0.036 5.62%
Month 35 3.263 35 0.995 3.281 3.553 3.534 -0.271 0.271 0.073 8.29%
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
1.005 1.016 1.011 0.997 0.985 98.55%
0.979 0.984 0.975 1.012 1.065 1.047
Average 0.977 0.986 1.003 1.013 1.035 1.040 1.013 1.005 1.013 1.003 0.995 98.40%
Forecasts for future periods
Period
Unseason
alized
forecast
Seasonal
index
Seasonali
zed
forecast
37.000 3.576 0.977 3.495
38.000 3.588 0.986 3.539
39.000 3.600 1.003 3.612
40.000 3.612 1.013 3.658
41.000 3.624 1.035 3.749
42.000 3.635 1.040 3.781
43.000 3.647 1.013 3.695
44.000 3.659 1.005 3.678
45.000 3.671 1.013 3.718
46.000 3.683 1.003 3.693
Problem 11-44
47.000 3.694 0.995 3.674
Period
Time
Centered
average
Seasonal
Seasonal
index
zed
Month 1 2.972 1 0.977 3.041 3.152 3.080 -0.108 0.108 0.012 3.64%
Month 2 2.955 2 0.986 2.997 3.164 3.120 -0.165 0.165 0.027 5.58%
Month 3 2.991 3 1.003 2.981 3.176 3.186 -0.195 0.195 0.038 6.53%
Month 4 3.117 4 1.013 3.078 3.187 3.228 -0.111 0.111 0.012 3.56%
Month 5 3.178 5 1.035 3.072 3.199 3.310 -0.132 0.132 0.017 4.14%
Month 6 3.148 6 1.040 3.027 3.211 3.339 -0.191 0.191 0.037 6.08%
Month 7 3.189 7 3.174 1.005 1.013 3.148 3.223 3.265 -0.076 0.076 0.006 2.39%
Month 8 3.255 8 3.205 1.016 1.005 3.238 3.234 3.251 0.004 0.004 0.000 0.12%