ICAEW BIP · Chapter 8 · Question 2 of 10
A company forecasts quarterly sales using an additive time series model. The trend is given by T = 2,400 + 35t, where t is the quarter number and t = 1 is quarter 1 of year 1. The average seasonal variations calculated from past data are: quarter 1 +210, quarter 2 -40, quarter 3 -190, quarter 4 +40. These must be adjusted so that they sum to zero before use. What is the sales forecast for quarter 3 of year 4?
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: D) 2,730 units
Explanation
Quarter 3 of year 4 is t = (3 x 4) + 3 = 15. Trend = 2,400 + (35 x 15) = 2,925. The seasonal variations sum to +20, so 20 / 4 = 5 is deducted from each, making the quarter 3 variation -195. Forecast = 2,925 - 195 = 2,730 units. Using the unadjusted variation gives 2,735, and using t = 14 gives 2,695.
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