Sales forecasting: time series and moving averages

Time series and their parts

A time series is a set of data recorded at regular intervals: monthly sales, quarterly revenue. It can be broken into:

• Trend: the underlying long-term direction.
• Seasonal variation: regular, predictable changes within a year (ice cream in summer, toys before festivals).
• Cyclical variation: longer swings linked to the economic cycle.
• Random variation: one-off events (a strike, extreme weather).

Moving averages remove the short-term fluctuations to reveal the trend.

Three-period moving average

Add three consecutive values, divide by 3, and place the result against the middle period. Then move on one period and repeat.

Monthly sales ($000): 42, 45, 51, 48, 54, 57, 60.

Each average is placed against the middle month. The trend is clearly upward.

Four-quarter moving average and centring

With quarterly data, use four quarters so that every average contains one of each season, which removes seasonal variation. The middle of four quarters falls between two quarters (the first lies between Q2 and Q3), so the two neighbouring four-quarter averages are averaged again to give a centred moving average that lines up with a quarter.

Four-quarter averages for the data below: 140, 142.5, 145.5, 149, 151.

Each centred value is the mean of a neighbouring pair of four-quarter averages. The trend rises steadily while sales swing with the seasons.

Seasonal variation and limitations

The seasonal variation for a quarter is actual value minus the centred trend: for Y1 Q3, 180 - 141.25 = 38.75. Averaging these for each quarter, then adding them to a projected trend, gives a seasonally adjusted forecast.

Limitations of moving averages:

• They assume past patterns will continue; sudden changes (a new competitor, a recession, a pandemic) are not predicted.
• The trend is lost at the ends of the series, the most recent and most useful part.
• They need plenty of reliable past data, so they suit established products, not new ones.
• They ignore the causes of change (prices, marketing, the economy), so qualitative judgement is still needed.

A real example

In the January 2024 WBS13 paper, Question 1(b) asked for the three-year moving average of the percentage of recycled material an outdoor clothing company used, centred on 2021. The figures for 2020, 2021 and 2022 were 65%, 66% and 72%: (65 + 66 + 72) / 3 = 203 / 3 = 67.67%. The mark scheme gave 1 mark for the method, 2 for using the right figures and 1 for the answer; 67.67 without the % sign and without working scored 3 out of 4.

Worked example

Quarterly sales are 120, 150, 180, 110, 130. Calculate the first two four-quarter moving averages and the first centred moving average.

1. First: (120 + 150 + 180 + 110) / 4 = 560 / 4 = 140.
2. Second: (150 + 180 + 110 + 130) / 4 = 570 / 4 = 142.5.
3. Centred: (140 + 142.5) / 2 = 141.25, placed against Y1 Q3.

Answer: 140 and 142.5; centred value 141.25.

Check yourself

1. Monthly sales (units) were 64, 70, 61, 73, 79, 70. Calculate the last three-month moving average.
   Show answer

   74.00 units. (73 + 79 + 70) / 3 = 222 / 3 = 74.00.

2. Quarterly sales (units) were 210, 260, 300, 190. Calculate the four-quarter moving average.
   Show answer

   240.0 units. (210 + 260 + 300 + 190) / 4 = 960 / 4 = 240.

3. Quarterly sales (units) were 210, 260, 300, 190, 230. Calculate the first centred moving average.
   Show answer

   242.50 units. Four-quarter averages: 960 / 4 = 240 and 980 / 4 = 245. Centred = (240 + 245) / 2 = 242.5.

4. Using the same data (210, 260, 300, 190, 230), the first centred average sits against the third quarter, whose actual sales were 300. Calculate the seasonal variation for that quarter.
   Show answer

   57.50 units. Actual - trend = 300 - 242.5 = 57.5. Sales are well above trend in this quarter.

5. January 2024 WBS13: an outdoor clothing company used 65%, 66% and 72% recycled material in 2020, 2021 and 2022. Calculate the three-year moving average for 2021, to 2 decimal places.
   Show answer

   67.67 %. (65 + 66 + 72) / 3 = 203 / 3 = 67.67%.

6. Why is a four-quarter moving average used for quarterly data?
   • Four is the largest number of values allowed
   • Each average contains one of every quarter, so seasonal variation is removed
   • It makes the trend steeper
   • It predicts random events
   Show answer

   Each average contains one of every quarter, so seasonal variation is removed. Including all four seasons cancels out seasonal highs and lows.

7. Which is a limitation of using moving averages to forecast sales?
   • They cannot be calculated with a calculator
   • They exaggerate seasonal variation
   • They only work for monthly data
   • They assume past patterns will continue into the future
   Show answer

   They assume past patterns will continue into the future. Sudden changes in the market are not predicted.

8. Explain one reason why an accurate sales forecast is useful to a business.
   Show answer

   It helps the business plan production and stock levels, so it can buy the right amount of materials and employ the right number of staff, avoiding waste or shortages and helping cash flow budgeting.. Name what it helps plan and the benefit.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Business specification (XBS11/YBS11, 2018), Unit 3 Business decisions and strategy and Appendices 6, 7 and 9
• Pearson Edexcel IAL Business WBS13/01 mark scheme, January 2024

Last updated 8 November 2026. Spotted a mistake? Tell us.