Topic 6 of 7 · Form 4
Time series and moving averages
Data recorded at intervals over time (monthly sales, quarterly rainfall); plotting time series graphs; identifying trend, seasonal variation and random fluctuations.
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Time series
Data recorded at intervals over time (monthly sales, quarterly rainfall); plotting time series graphs; identifying trend, seasonal variation and random fluctuations.
Moving averages
Smooth out seasonal variation to show the trend. For quarterly data use 4-point moving averages, centred between quarters (centred moving averages average two consecutive 4-point averages).
Worked example: Quarterly sales: 12, 18, 20, 14, 16, 22. Find the 4-point moving averages and the centred values.
4-point totals: 64, 68, 72 → averages 16, 17, 18; centred averages 16.5 and 17.5
Trend line and seasonal variation
Plot moving averages and draw a trend line; seasonal variation = actual value − trend value; average seasonal variation for each quarter.
Forecasting
Extend the trend line and add the average seasonal variation; forecasts become less reliable further ahead.
Worked example: The trend for Quarter 3 next year is predicted to be 25 and the average seasonal variation for Quarter 3 is +3. Forecast the value.
25 + 3 = 28
Check yourself
- Why are 4-point moving averages used for quarterly data?
- What is seasonal variation?
- Why are long-term forecasts unreliable?
Show answers
- Each average covers a full year, removing seasonal effects.
- The regular difference between actual values and the trend for a particular season.
- Conditions may change and errors in the trend become larger further ahead.
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