Cambridge IGCSE Statistics 12: Time series
Cambridge IGCSE Statistics 0479 notes on time series.
Cambridge IGCSE Statistics 0479 Topic 12 covers time-series graphs, moving averages and centring, trend, seasonal components, prediction, and the assumptions and limitations behind forecasts.
1. Time-series structure
A time series records one variable in chronological order, usually at equal intervals. Its observed movement may contain:
- trend, the longer-term direction
- seasonal variation, a pattern repeating at a fixed known period
- irregular variation, unpredictable short-term movement
A rise followed by a fall is not automatically seasonal. Seasonality requires repetition at corresponding positions in successive cycles.
2. Plotting a time-series graph
Put time on the horizontal axis and the measured variable, with units, vertically. Use a consistent time scale and plot in chronological order. Joining successive points is appropriate because sequence is part of the data, unlike a scatter diagram.
Choose a scale that shows variation without distorting it. If a vertical-axis break is used, make it explicit. Label years, quarters or months carefully so observations are not shifted by one period.
The raw graph helps identify overall direction, seasonal repetition, turning points and unusual values, but short-term fluctuations can obscure trend.
3. Moving averages
A moving average smooths irregular and seasonal variation by averaging consecutive observations. Choose a span matching the seasonal cycle: four quarters, twelve months, or another stated period.
For a four-point moving average, average observations 1 to 4, then 2 to 5, then 3 to 6, continuing one period at a time. Every window must contain exactly four values.
Moving averages lose observations at both ends because complete windows are unavailable there. This is a structural consequence, not a calculation mistake.
4. Positioning and centring
An odd-span moving average lies naturally at its middle time point. A three-point average of periods 1 to 3 is plotted at period 2.
An even-span average lies between two time points. A four-point average for periods 1 to 4 lies between periods 2 and 3, so it does not align with an original observation. Centre it by averaging two adjacent four-point moving averages. The resulting centred moving average aligns with the shared intervening period.
Centre only when alignment requires it. Do not centre an already aligned odd-span series automatically.
5. Trend
Centred moving averages estimate the trend-cycle component by smoothing seasonal effects. Plot them at correct time positions and draw a trend line by eye through their central pattern when requested.
