Moving averages

Sauce Co manufactures and sells cartons of cooking sauces. The finance director would like to forecast sales, including the impact of seasonal variation.

Data has been gathered and the following centered moving averages have been calculated, using a base period of 4 quarters. The seasonal variations are 0·904 for quarter 3 and 1·079 for quarter 4. The random component is negligible and can therefore be ignored.

YEAR ‘000 Units

Quarter 1 Quarter 2 Quarter 3 Quarter 4

20×2 1,086.75 1,112.5 1,162.5 1,206.25

20×3 1,243.75 1,287.5

What are the forecast sales for 20×3, Quarters 3 & 4 (to the nearest whole number)?

ANSWER:
Step 1:
Calculate the average trend of the centred moving averages:
(1,287.5 – 1,086.75)/5 = 40,150 units per quarter

Step 2:
Add the average to quarters 3 and 4 to extend the trend:
Quarter 3: 1,287,500 + 40,150 = 1,327,650
Quarter 4: 1,287,500 + (40,150 * 2) = 1,367,800

Step 3:
Apply the season variation:
Quarter 3: 1,327,650 * 0.904 = 1,200,196
Quarter 4: 1,367,800 * 1.079 = 1,475,856

If you got the wrong answers, you calculated the average trend by dividing by 6, not 5.

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From the video I watched, I understood that once we calculate the centered moving average, we subtract that from the actual from the trend to get the variation…

So I’m already stuck on step 1. If its quarterly, why are we diving by 5 and why would be accidently divide by 6. And these are not actuals, they are already the centered moving average :S