Homework Answers
a) The calculation are given below in table
| S.No | Year | Time Series (Yt) | MA(4) | CMA | RTMA= Yt/CMA | S-Index | Dt=Yt/S-Index | Trend=-2.970+5.475X | |
| 1 | Year1 | Quarter 1 | 9 | 0.97 | 9.28 | -2.97 | |||
| 2 | Quarter 2 | 5 | 0.59 | 8.47 | 2.51 | ||||
| 3 | Quarter 3 | 15 | 13.75 | 15.13 | 0.99 | 1.02 | 14.71 | 7.98 | |
| 4 | Quarter 4 | 26 | 16.50 | 17.38 | 1.5 | 1.41 | 18.44 | 13.46 | |
| 5 | Year2 | Quarter 1 | 20 | 18.25 | 20.63 | 0.97 | 0.97 | 20.62 | 18.93 |
| 6 | Quarter 2 | 12 | 23.00 | 26.13 | 0.46 | 0.59 | 20.34 | 24.41 | |
| 7 | Quarter 3 | 34 | 29.25 | 32.25 | 1.05 | 1.02 | 33.33 | 29.88 | |
| 8 | Quarter 4 | 51 | 35.25 | 38.50 | 1.32 | 1.41 | 36.17 | 35.36 | |
| 9 | Year3 | Quarter 1 | 44 | 41.75 | 45.25 | 0.97 | 0.97 | 45.36 | 40.83 |
| 10 | Quarter 2 | 38 | 48.75 | 52.88 | 0.72 | 0.59 | 64.41 | 46.31 | |
| 11 | Quarter 3 | 62 | 57.00 | 1.02 | 60.78 | 51.78 | |||
| 12 | Quarter 4 | 84 | 1.41 | 59.57 | 237.74 | ||||
| 13 | Year4 | Quarter 1 | 239.40 | ||||||
| 14 | Quarter 2 | 241.05 | |||||||
| 15 | Quarter 3 | 242.71 | |||||||
| 16 | Quarter 4 | 244.37 |
where MA(4) = moving average for four periods
CMA = center moving average
RTMA = Ration to moving Average
S- index = is seasonal index
Dt = Deseasonalized index
Yt = time series
The Seasonal indexes are given below in the table
| Year 1 | Year 2 | Year 3 | Average | |
| Quarter 1 | 0.97 | 0.97 | 0.97 | |
| Quarter 2 | 0.46 | 0.72 | 0.59 | |
| Quarter 3 | 0.99 | 1.05 | 1.02 | |
| Quarter 4 | 1.5 | 1.32 | 1.41 |
b) The trend line equation is
Trend=-2.970+5.475X
and the forecasts are given below in the table
| Time period | Forecast | |
| 13 | Quarter 1 | 239.4 |
| 14 | Quarter 2 | 241.05 |
| 15 | Quarter 3 | 242.71 |
| 16 | Quarter 4 | 244.37 |
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