This is a simple problem related to creation of a forecasting model with seasonal effects taken into account.
This kind of a forecasting model is done with the help of Holt's winter's seasonal model which taken into account the seasonal impact on calculaton.
To derive the desired forecast ,we use the following formula for Holt's winter model .
Based on the formula application ,we have traced the forecast for the next 8 quarters along with the sensitivity analysis.
Winter's Model | ||||||||
alpha = | 0.50 | |||||||
beta = | 0.30 | |||||||
period | sales | level | trend | forecast | error | ABS(error) | Squared Error | Percent Error |
1 | 52 | 52 | 0 | - | - | - | - | - |
2 | 46 | 52 | 0 | 52.00 | -6.00 | 6.00 | 36.00 | 0.13 |
3 | 56 | 49.00 | -0.90 | 48.10 | 7.90 | 7.90 | 62.41 | 0.14 |
4 | 75 | 52.05 | 0.28 | 52.34 | 22.67 | 22.67 | 513.70 | 0.30 |
5 | 92 | 63.67 | 3.68 | 67.35 | 24.65 | 24.65 | 607.51 | 0.27 |
6 | 65 | 79.68 | 7.38 | 87.06 | -22.06 | 22.06 | 486.56 | 0.34 |
7 | 50 | 76.03 | 4.07 | 80.10 | -30.10 | 30.10 | 906.14 | 0.60 |
8 | 60 | 65.05 | -0.44 | 64.61 | -4.61 | 4.61 | 21.24 | 0.08 |
9 | 81 | 62.30 | -1.13 | 61.17 | 19.83 | 19.83 | 393.19 | 0.24 |
10 | 108 | 71.09 | 1.84 | 72.93 | 35.07 | 35.07 | 1230.16 | 0.32 |
11 | 74 | 90.46 | 7.10 | 97.57 | -23.57 | 23.57 | 555.31 | 0.32 |
12 | 49 | 85.78 | 3.57 | 89.35 | -40.35 | 40.35 | 1628.10 | 0.82 |
13 | 59 | 69.17 | -2.49 | 66.69 | -7.69 | 7.69 | 59.13 | 0.13 |
14 | 79 | 62.84 | -3.64 | 59.21 | 19.79 | 19.79 | 391.80 | 0.25 |
15 | 102 | 69.10 | -0.67 | 68.43 | 33.57 | 33.57 | 1126.72 | 0.33 |
16 | 73 | 85.22 | 4.37 | 89.58 | -16.58 | 16.58 | 274.96 | 0.23 |
17 | 89.58 | 81.29 | 1.88 | 83.17 | 6.41 | 6.41 | 41.13 | 0.07 |
18 | 83.17 | 86.38 | 2.84 | 89.22 | -6.05 | 6.05 | 36.56 | 0.07 |
19 | 89.22 | 86.19 | 1.93 | 88.13 | 1.09 | 1.09 | 1.19 | 0.01 |
20 | 88.13 | 88.67 | 2.10 | 90.77 | -2.64 | 2.64 | 6.98 | 0.03 |
21 | 90.77 | 89.45 | 1.70 | 91.15 | -0.38 | 0.38 | 0.14 | 0.00 |
22 | 91.15 | 90.96 | 1.64 | 92.60 | -1.45 | 1.45 | 2.11 | 0.02 |
23 | 92.60 | 91.87 | 1.43 | 93.30 | -0.70 | 0.70 | 0.49 | 0.01 |
24 | 93.30 | 92.95 | 1.32 | 94.27 | -0.97 | 0.97 | 0.94 | 0.01 |
-1.51 | 21.53 | 585.48 | 0.32 | |||||
BIAS | MAD | MSE | MAPE |
A popular brand of fly fishing rods has had the following demand history by quarters for the past 16 quarters. Quarter Demand Quarter Demand 81 52 1 9 46 10 108 56 74 12 49 4 75 13 59 5 92 14 6 65 79...
A popular brand of fly fishing rods has had the following demand history by quarters for the past 16 quarters. Quarter Demand Quarter Demand 1 52 9 81 2 46 10 108 3 56 11 74 4 75 12 49 5 92 13 59 6 65 14 79 7 50 15 102 8 60 16 73 a. Using the data above, forecast the demand for the next 8 quarters using Winter’s Seasonal Model. Use Minitab to find a good fitting...