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- 16 Marks
Question
Quarterly sales of a Golden Tree Chocolate Bar at a popular mall in KoKoLand City are given as follows:
| YEAR | QUARTER 1 | QUARTER 2 | QUARTER 3 | QUARTER 4 |
|---|---|---|---|---|
| 1 | 1260 | 756 | 588 | 1596 |
| 2 | 1352 | 966 | 579 | 2028 |
| 3 | 1786 | 920 | 865 | 2273 |
Required:
(i) Calculate the trend in the series using a 4-point centered moving average method. (4 Marks)
(ii) Using (i), calculate the Average Seasonal Variation based on the Additive Model of Time Series analysis. (4 Marks)
(iii) Using the values in (ii), determine the Adjusted Average Seasonal Variation for the Time Series Data. (4 Marks)
(iv) Prepare Seasonal Adjusted Forecast for Year 4 using the Additive Model. (4 Marks)
Answer
(i) Calculation of Trend using a 4-point centered moving average method:
| TIME | SALES (A) | 4-POINT MOVING TOTAL | 4-POINT MOVING AVERAGE | CENTERED MOVING AVERAGE (T) | SEASONAL EFFECT (A-T) |
|---|---|---|---|---|---|
| 1 | 1260 | ||||
| 2 | 756 | 4200 | 1050.00 | ||
| 3 | 588 | 4292 | 1073.00 | 1062 | -474 |
| 4 | 1596 | 4502 | 1125.50 | 1099 | 497 |
| 5 | 1352 | 4495 | 1123.25 | 1124 | 228 |
| 6 | 966 | 4925 | 1231.25 | 1177 | -211 |
| 7 | 579 | 5359 | 1339.75 | 1286 | -707 |
| 8 | 2028 | 5513 | 1328.75 | 1334 | 694 |
| 9 | 1786 | 5599 | 1399.75 | 1364 | 422 |
| 10 | 920 | 5844 | 1461.00 | 1430 | -510 |
| 11 | 865 | ||||
| 12 | 2273 |
(ii) Calculation of Average Seasonal Variation based on the Additive Model:
| YEAR | QUARTER 1 | QUARTER 2 | QUARTER 3 | QUARTER 4 |
|---|---|---|---|---|
| 1 | -474 | 497 | ||
| 2 | 228 | -211 | -707 | 694 |
| 3 | 422 | -510 |
| TOTAL | 650 | -721 | -1181 | 1191 |
| AVERAGE | 325 | -360.5 | -590.5 | 595.5 |
(iii) Adjusted Average Seasonal Variation:
| QUARTER | AVERAGE | ADJUSTMENT FACTOR | ADJUSTED AVERAGE SEASONAL EFFECT |
|---|---|---|---|
| 1 | 325.00 | + 7.625 | 332.625 |
| 2 | -360.50 | + 7.625 | -352.875 |
| 3 | -590.50 | + 7.625 | -582.875 |
| 4 | 595.50 | + 7.625 | 603.125 |
(iv) Seasonal Adjusted Forecast for Year 4:
| YEAR | QUARTER | PERIOD | TREND | SEASONAL EFFECT | FORECAST |
|---|---|---|---|---|---|
| 4 | 1 | 13 | 1590 | +333 | 1923 |
| 4 | 2 | 14 | 1645 | -353 | 1292 |
| 4 | 3 | 15 | 1700 | -583 | 1117 |
| 4 | 4 | 16 | 1755 | +603 | 2358 |
The trend column above was obtained by computing the gradient using the first value of the centered moving average (1062) and the last centered moving average (1430).
The gradient = (1430 – 1062) / (10 – 3) = 52.57.
Forecasting from the last centered moving average, we evaluate the equation:
1430 + 52.57 * (x – 3), where x = 3, 4, 5, 6.
Example: Trend value of the first quarter of Year 4 is given by:
1430 + 52.57 * (3) = 1587.71 ≈ 1590.
- Tags: Additive model, Forecasting, Seasonal Variation, Time series, Trend Analysis
- Level: Level 1
- Topic: Forecasting
- Series: NOV 2015
- Uploader: Joseph