- 20 Marks
Question
The following data is number of bars of chocolate consumed by ladies in a tertiary institution in Ga-East Municipal area.
| T | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Y | 986 | 1245 | 902 | 704 | 812 | 1048 | 706 | 514 |
| (a) Explain the terms de-seasonalized trend, seasonal index and forecast value in relation to the data above. [7 Marks] | ||||||||
| (b) Forecast with seasonality and average trend the values for the next four periods of the above time series. [18 Marks] |
Answer
| (a) De-seasonalized trend: The underlying long-term movement in the data after removing seasonal effects, e.g., for chocolate consumption, adjusting quarterly fluctuations to reveal if overall intake is declining due to health trends. Seasonal index: A factor showing how each period deviates from average, e.g., higher index in period 2 might indicate peak consumption during holidays. Forecast value: Predicted future value using trend and seasonality, e.g., projecting next quarter’s consumption for inventory planning in banking-related supply chain finance. |
(b) Assuming quarterly data (4 seasons), use multiplicative model. Seasonal indices: Calculate averages per season: S1=(986+812)/2=899, S2=1146.5, S3=804, S4=609. Grand avg=865.375. Indices: SI1=899/865.375≈1.04, SI2≈1.33, SI3≈0.93, SI4≈0.70. De-seasonalized: Divide Y by SI: [948.3, 938.9, 970.0, 999.5, 781.0, 790.3, 759.2, 729.7]. Fit linear trend to de-seasonalized: slope≈-37.93, intercept≈1035.29. Equation: Trend_t = 1035.29 – 37.93t. For t=9-12: Trends [693.0, 655.1, 617.2, 579.3]. Forecasts: Multiply by SI: Period9 (SI1)≈721.5,10(SI2)≈869.9,11(SI3)≈574.8,12(SI4)≈408.7.
To arrive: Seasonal indices via averages normalized. De-seasonalize Y/SI. Least squares on t vs. de-seasonalized for trend (as “average trend” may imply linear fit to adjusted data). Forecast = Trend * SI. This aids in predicting demand for consumer lending products tied to seasonal spending in Ghana.
- Topic: seasonal variation and random variation)
- Series: APR 2023
- Uploader: Samuel Duah