In: Statistics and Probability
Deseasonalize the data and use an appropriate technique to find the seasonally unadjusted forecasts for the next year. Include your results here, showing the deseasonalized data and the seasonally unadjusted forecasts.
Period |
Year |
Quarter |
Sales |
1 |
1 |
1 |
40 |
2 |
1 |
2 |
60 |
3 |
1 |
3 |
65 |
4 |
1 |
4 |
80 |
5 |
2 |
1 |
44 |
6 |
2 |
2 |
70 |
7 |
2 |
3 |
72 |
8 |
2 |
4 |
91 |
9 |
3 |
1 |
46 |
10 |
3 |
2 |
77 |
11 |
3 |
3 |
74 |
12 |
3 |
4 |
100 |
13 |
4 |
1 |
50 |
14 |
4 |
2 |
80 |
15 |
4 |
3 |
83 |
16 |
4 |
4 |
109 |
The calculations are:
Centered | |||||||
Moving | Ratio to | Seasonal | Sales | ||||
t | Year | Quarter | Sales | Average | CMA | Indexes | Deseasonalized |
1 | 1 | 1 | 40 | 0.653 | 61.2 | ||
2 | 1 | 2 | 60 | 1.031 | 58.2 | ||
3 | 1 | 3 | 65 | 61.750 | 1.053 | 1.026 | 63.3 |
4 | 1 | 4 | 80 | 63.500 | 1.260 | 1.290 | 62.0 |
5 | 2 | 1 | 44 | 65.625 | 0.670 | 0.653 | 67.4 |
6 | 2 | 2 | 70 | 67.875 | 1.031 | 1.031 | 67.9 |
7 | 2 | 3 | 72 | 69.500 | 1.036 | 1.026 | 70.2 |
8 | 2 | 4 | 91 | 70.625 | 1.288 | 1.290 | 70.5 |
9 | 3 | 1 | 46 | 71.750 | 0.641 | 0.653 | 70.4 |
10 | 3 | 2 | 77 | 73.125 | 1.053 | 1.031 | 74.7 |
11 | 3 | 3 | 74 | 74.750 | 0.990 | 1.026 | 72.1 |
12 | 3 | 4 | 100 | 75.625 | 1.322 | 1.290 | 77.5 |
13 | 4 | 1 | 50 | 77.125 | 0.648 | 0.653 | 76.5 |
14 | 4 | 2 | 80 | 79.375 | 1.008 | 1.031 | 77.6 |
15 | 4 | 3 | 83 | 1.026 | 80.9 | ||
16 | 4 | 4 | 109 | 1.290 | 84.5 |
The forecasts are:
Forecast |
50.54341 |
79.74376 |
79.39294 |
99.81989 |