Analyse trend and seasonality in time series
Plot time-ordered data, smooth short-term variation with moving averages, estimate seasonal effects and make qualified predictions.
Section Paper 2 · Written · calculator required
Exam scope and assessment notes
This lesson maps the Analyse trend and seasonality in time series section of Cambridge IGCSE Statistics 0479 (2027 and 2028–2030 syllabus versions). This is original StudyForA teaching and self-check practice, not Cambridge material, an official mark scheme, a timed mock or an official grade. Charts and written working are not automatically assessed; human subject-teacher review remains pending. Use the syllabus version for your exam year. Cambridge offers 0479 in the June series only and does not make it available in every administrative zone. Check the current Cambridge 0479 page and confirm your centre's entry eligibility with your exams officer.
Before you begin
- Use the earlier 0479 ideas where needed; write units, working and a contextual interpretation for each result.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Find the 3-point moving average of 10, 13 and 16.
What you will learn
- Plot a time-series graph
- Explain why moving averages are used
- Calculate, plot and centre moving averages where appropriate
- Describe trend and draw a trend line using moving averages
- Calculate average seasonal components
- Predict using trend and seasonality while stating assumptions and limitations
Keep time order visible
A time-series graph plots a measured value against time in chronological order. Label both axes and use consistent time intervals. A trend is the longer-term direction; seasonal variation is a repeating pattern within a fixed period, such as months or quarters.
Moving averages smooth short-term variation
For a period of length k, average each consecutive window of k observations and plot it at the window's time centre. With an even period, the first moving averages lie between time points; centre them by averaging adjacent moving averages, then plot at an actual time point. The amount of smoothing should match the seasonal cycle.
Estimate seasonal components and predict cautiously
A seasonal component is the typical within-cycle difference from the trend. With an additive model, subtract the trend or centred moving average from each observation, then average those differences by season. Seasonal components should approximately sum to zero across one complete cycle.
A prediction combines a projected trend with the corresponding seasonal component. It assumes the past trend and seasonal pattern continue; unusual events, structural changes and small datasets can make forecasts unreliable.
Pause and explain
If a quarter's average seasonal component is −5, how does it affect a trend-based forecast under an additive model?
Worked example
Quarterly values have centred trend estimates 20, 22, 24, 26 and observed values 23, 20, 28, 23. Find each seasonal component using observed minus trend.
Show the worked solution
- Quarter 1: 23−20=+3.
- Quarter 2: 20−22=−2.
- Quarter 3: 28−24=+4.
- Quarter 4: 23−26=−3.
Answer The seasonal components are +3, −2, +4 and −3. They sum to 2, not zero, because these are one observed cycle; longer data would usually be used to average each season and reduce irregular variation.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Monthly sales for three consecutive months are 12, 18 and 15 thousand units. Find the 3-month moving average and state where it is plotted.
Give me a hint
Average the three values and place the result at the centre month.
Compare my reasoning
- Average = (12+18+15)/3 = 15.
- The window covers three months.
- Plot 15 at the second, centre month.
The moving average is 15 thousand units and is plotted at the middle month.
Look for these in your work
- Mean correct
- Units retained
- Time position correct
Four-quarter moving averages are 40, 44 and 48. Find the centred moving averages and explain their time positions.
Give me a hint
Average adjacent four-quarter values because each original average sits halfway between quarter points.
Compare my reasoning
- First centred value = (40+44)/2 = 42.
- Second centred value = (44+48)/2 = 46.
- Each centred value aligns with an actual quarter between the two original average positions.
The centred moving averages are 42 and 46. Averaging neighbouring four-quarter values moves the smoothed estimates from half-quarter positions to actual quarter positions.
Look for these in your work
- Both averages correct
- Centring rule used
- Alignment explained
A trend estimate for next winter is 90 units and the average winter seasonal component is +12. Give the forecast and one assumption that could make it unreliable.
Give me a hint
Use forecast = trend + seasonal component.
Compare my reasoning
- Forecast = 90 + 12 = 102 units.
- The method assumes the trend continues.
- A major change in demand or supply could disrupt the historical seasonal pattern.
The forecast is 102 units under the additive model. It may be unreliable if the trend or winter pattern changes, for example after a major supply disruption.
Look for these in your work
- Additive forecast correct
- Units stated
- Assumption and limitation stated
Common mistakes
- Plotting time in a non-chronological order
- Plotting an even-period moving average at a half period without centring
- Calling every rise a seasonal effect without a repeating cycle
- Making a forecast without naming the continuation assumption
What can you explain now?
Why are adjacent moving averages centred when the period length is even?
Compare with the explanation
Their midpoints fall between observations, so averaging adjacent values aligns the result with a time point
Centring places the smoothed value at a meaningful plotted time.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
When do you centre moving averages, and how does an additive seasonal component change a trend forecast?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.